Partial differential equations and solitary waves theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Beijing
Higher Education Press
2009
Berlin [u.a.] Springer |
| Series: | Nonlinear physical science
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIX, 741 S. graph. Darst. 24 cm |
| ISBN: | 9787040254808 9783642002502 |
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| 245 | 1 | 0 | |a Partial differential equations and solitary waves theory |c Abdul-Majid Wazwaz |
| 264 | 1 | |a Beijing |b Higher Education Press |c 2009 | |
| 264 | 1 | |a Berlin [u.a.] |b Springer | |
| 300 | |a XIX, 741 S. |b graph. Darst. |c 24 cm | ||
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CONTENTS PART I PARTIAL DIFFERENTIAL EQUATIONS 1 BASIC CONCEPTS 3 1. 1
INTRODUCTION 3 1.2 DEFINITIONS 4 .2.1 DEFINITION OF A PDE 4 .2.2 ORDER
OF A PDE 5 .2.3 LINEAR AND NONLINEAR PDES 6 .2.4 SOME LINEAR PARTIAL
DIFFERENTIAL EQUATIONS 7 .2.5 SOME NONLINEAR PARTIAL DIFFERENTIAL
EQUATIONS 7 .2.6 HOMOGENEOUS AND INHONIOGENEOUS PDES 9 .2.7 SOLUTION OF
A PDE. 9 .2.8 BOUNDARY CONDITIONS 11 .2.9 INITIAL CONDITIONS 12 1.2.10
WELL-POSED PDES 12 1.3 CLASSIFICATIONS OF A SECOND-ORDER PDE 14
REFERENCES 17 2 FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS 19 2.1
INTRODUCTION 19 2.2 ADOMIAN DECOMPOSITION METHOD 19 2.3 THE NOISE TERMS
PHENOMENON 36 2.4 THE MODIFIED DECOMPOSITION METHOD 41 2.5 THE
VARIATIONAL ITERATION METHOD 47 2.6 METHOD OF CHARACTERISTICS 54 2.7
SYSTEMS OF LINEAR PDES BY ADOMIAN METHOD 59 2.8 SYSTEMS OF LINEAR PDES
BY VARIATIONAL ITERATION METHOD 63 REFERENCES. 68 BIBLIOGRAFISCHE
INFORMATIONEN HTTP://D-NB.INFO/992291526 DIGITALISIERT DURCH XII
CONTENTS 3 ONE DIMENSIONAL HEAT FLOW 69 3.1 INTRODUCTION 69 3.2 THE
ADOMIAN DECOMPOSITION METHOD 70 3.2.1 HOMOGENEOUS HEAT EQUATIONS 73
3.2.2 INHOMOGENEOUS HEAT EQUATIONS 80 3.3 THE VARIATIONAL ITERATION
METHOD 83 3.3.1 HOMOGENEOUS HEAT EQUATIONS 84 3.3.2 INHOMOGENEOUS HEAT
EQUATIONS 87 3.4 METHOD OF SEPARATION OF VARIABLES 89 3.4.1 ANALYSIS OF
THE METHOD 89 3.4.2 INHOMOGENEOUS BOUNDARY CONDITIONS 99 3.4.3 EQUATIONS
WITH LATERAL HEAT LOSS 102 REFERENCES 106 4 HIGHER DIMENSIONAL HEAT FLOW
107 4.1 INTRODUCTION 107 4.2 ADOMIAN DECOMPOSITION METHOD 108 4.2.1 TWO
DIMENSIONAL HEAT FLOW 108 4.2.2 THREE DIMENSIONAL HEAT FLOW 116 4.3
METHOD OF SEPARATION OF VARIABLES 124 4.3.1 TWO DIMENSIONAL HEAT FLOW
124 4.3.2 THREE DIMENSIONAL HEAT HOW 134 REFERENCES 140 5 ONE
DIMENSIONAL WAVE EQUATION 143 5.1 INTRODUCTION 143 5.2 ADOMIAN
DECOMPOSITION METHOD 144 5.2.1 HOMOGENEOUS WAVE EQUATIONS 146 5.2.2
INHOMOGENEOUS WAVE EQUATIONS 152 5.2.3 WAVE EQUATION IN AN INFINITE
DOMAIN 157 5.3 THE VARIATIONAL ITERATION METHOD 162 5.3.1 HOMOGENEOUS
WAVE EQUATIONS 162 5.3.2 INHOMOGENEOUS WAVE EQUATIONS 168 5.3.3 WAVE
EQUATION IN AN INFINITE DOMAIN 170 5.4 METHOD OF SEPARATION OF VARIABLES
174 5.4.1 ANALYSIS OF THE METHOD 174 5.4. CONTENTS 6.3 METHOD OF
SEPARATION OF VARIABLES 220 6.3.1 TWO DIMENSIONAL WAVE EQUATION 221
6.3.2 THREE DIMENSIONAL WAVE EQUATION 231 REFERENCES 236 LAPLACE'S
EQUATION 237 7.1 INTRODUCTION 237 7.2 ADOMIAN DECOMPOSITION METHOD 238
7.2.1 TWO DIMENSIONAL LAPLACE'S EQUATION 238 7.3 THE VARIATIONAL
ITERATION METHOD 247 7.4 METHOD OF SEPARATION OF VARIABLES 251 7.4.1
LAPLACE'S EQUATION IN TWO DIMENSIONS 251 7.4.2 LAPLACE'S EQUATION IN
THREE DIMENSIONS 259 7.5 LAPLACE'S EQUATION IN POLAR COORDINATES 267
7.5.1 LAPLACE'S EQUATION FOR A DISC 268 7.5.2 LAPLACE'S EQUATION FOR AN
ANNULUS 275 REFERENCES 283 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS 285
8.1 INTRODUCTION 285 8.2 ADOMIAN DECOMPOSITION METHOD 287 8.2.1
CALCULATION OF ADOMIAN POLYNOMIALS 288 8.2.2 ALTERNATIVE ALGORITHM FOR
CALCULATING ADOMIAN POLYNOMIALS 292 8.3 NONLINEAR ODES BY ADOMIAN METHOD
301 8.4 NONLINEAR ODES BY VIM 312 8.5 NONLINEAR PDES BY ADOMIAN METHOD
319 8.6 NONLINEAR PDES BY VIM 334 8.7 NONLINEAR PDES SYSTEMS BY ADOMIAN
METHOD 341 8.8 SYSTEMS OF NONLINEAR PDES BY VIM 347 REFERENCES 351
LINEAR AND NONLINEAR PHYSICAL MODELS 353 9.1 INTRODUCTION 353 9.2 THE
NONLINEAR ADVECTION PROBLEM 354 9.3 THE GOURSAT PROBLEM 360 9.4 THE
KLEIN-GORDON EQUATION 370 9.4. XIV CONTENTS 9.8 KORTEWEG-DEVRIES
EQUATION 401 9.9 FOURTH-ORDER PARABOLIC EQUATION 405 9.9.1 EQUATIONS
WITH CONSTANT COEFFICIENTS 405 9.9.2 EQUATIONS WITH VARIABLE
COEFFICIENTS 408 REFERENCES 413 10 NUMERICAL APPLICATIONS AND PADE
APPROXIMANTS 415 10.1 INTRODUCTION 415 10.2 ORDINARY DIFFERENTIAL
EQUATIONS 416 10.2.1 PERTURBATION PROBLEMS 416 10.2.2 NONPERTURBED
PROBLEMS 421 10.3 PARTIAL DIFFERENTIAL EQUATIONS 427 10.4 THE PADE
APPROXIMANTS 430 10.5 PADE APPROXIMANTS AND BOUNDARY VALUE PROBLEMS 439
REFERENCES 455 11 SOLITONS AND COMPACTONS 457 11.1 INTRODUCTION 457 11.2
SOLITONS 459 11.2.1 THE KDV EQUATION 460 11.2.2 THE MODIFIED KDV
EQUATION 462 11.2.3 THE GENERALIZED KDV EQUATION 464 11.2.4 THE
SINE-GORDON EQUATION 464 11.2.5 THE BOUSSINESQ EQUATION 465 11.2.6 THE
KADOMTSEV-PETVIASHVILI EQUATION 467 11.3 COMPACTONS 469 11.4 THE
DEFOCUSING BRANCH OF K(,N) 474 REFERENCES 475 PART N SOLITRAY WAVES
THEORY 12 SOLITARY WAVES THEORY 479 12.1 INTRODUCTION 479 12.2
DEFINITIONS 480 12.2.1 DISPERSION AND DISSIPATION 482 12.2.2 TYPES OF
TRAVELLING WAVE SOLUTIONS 484 12.2.3 NONANALYTIC SOLITARY WAVE SOLUTIONS
490 12.3 ANALYSIS OF THE METHODS 491 12.3.1 THE TANH-COTH METHOD 491
12.3.2 THE SINE-COSINE METHOD 493 12.3. CONTENTS XV 13 THE FAMILY OF THE
KDV EQUATIONS 503 13.1 INTRODUCTION 503 13.2 THE FAMILY OF THE KDV
EQUATIONS 505 13.2.1 THIRD-ORDER KDV EQUATIONS 505 13.2.2 THE K(N,N)
EQUATION 507 13.3 THE KDV EQUATION 507 13.3.1 USING THE TANH-COTH METHOD
508 13.3.2 USING THE SINE-COSINE METHOD 510 13.3.3 MULTIPLE-SOLITON
SOLUTIONS OF THE KDV EQUATION 510 13.4 THE MODIFIED KDV EQUATION 518
13.4.1 USING THE TANH-COTH METHOD 519 13.4.2 USING THE SINE-COSINE
METHOD 520 13.4.3 MULTIPLE-SOLITON SOLUTIONS OF THE MKDV EQUATION 521
13.5 SINGULAR SOLITON SOLUTIONS 523 13.6 THE GENERALIZED KDV EQUATION
526 13.6.1 USING THE TANH-COTH METHOD 526 13.6.2 USING THE SINE-COSINE
METHOD 528 13.7 THE POTENTIAL KDV EQUATION 528 13.7.1 USING THE
TANH-COTH METHOD 529 13.7.2 MULTIPLE-SOLITON SOLUTIONS OF THE POTENTIAL
KDV EQUATION 531 13.8 THE GARDNER EQUATION 533 13.8.1 THE KINK SOLUTION
533 13.8.2 THE SOLITON SOLUTION 534 13.8.3 N-SOLITON SOLUTIONS OF THE
POSITIVE GARDNER EQUATION. 535 13.8.4 SINGULAR SOLITON SOLUTIONS 537
13.9 GENERALIZED KDV EQUATION WITH TWO POWER NONLINEARITIES 542 13.9.1
USING THE TANH METHOD 543 13.9.2 USING THE SINE-COSINE METHOD 544 13.10
COMPACTONS: SOLITONS WITH COMPACT SUPPORT 544 13.10.1 THE K(N,N)
EQUATION 546 13.11 VARIANTS OF THE K(N,N) EQUATION 547 13.11. X VI
CONTENTS 14 KDV AND MKDV EQUATIONS OF HIGHER-ORDERS 557 14.1
INTRODUCTION 557 14.2 FAMILY OF HIGHER-ORDER KDV EQUATIONS 558 14.2.1
FIFTH-ORDER KDV EQUATIONS 558 14.2.2 SEVENTH-ORDER KDV EQUATIONS 561
14.2.3 NINTH-ORDER KDV EQUATIONS 562 14.3 FIFTH-ORDER KDV EQUATIONS 562
14.3.1 USING THE TANH-COTH METHOD 563 14.3.2 THE FIRST CONDITION 564
14.3.3 THE SECOND CONDITION 566 14.3.4 IV-SOLITON SOLUTIONS OF THE
FIFTH-ORDER KDV EQUATIONS . 567 14.4 SEVENTH-ORDER KDV EQUATIONS 576
14.4.1 USING THE TANH-COTH METHOD 576 14.4.2 V-SOLITON SOLUTIONS OF THE
SEVENTH-ORDER KDV EQUATIONS. 578 14.5 NINTH-ORDER KDV EQUATIONS 582
14.5.1 USING THE TANH-COTH METHOD 583 14.5.2 THE SOLITON SOLUTIONS 584
14.6 FAMILY OF HIGHER-ORDER MKDV EQUATIONS 585 14.6.1 IV-SOLITON
SOLUTIONS FOR FIFTH-ORDER MKDV EQUATION 586 14.6.2 SINGULAR SOLITON
SOLUTIONS FOR FIFTH-ORDER MKDV EQUATION 587 14.6.3 IV-SOLITON SOLUTIONS
FOR THE SEVENTH-ORDER MKDV EQUATION 589 14.7 COMPLEX SOLUTION FOR THE
SEVENTH-ORDER MKDV EQUATIONS 591 14.8 THE HIROTA-SATSUMA EQUATIONS 592
14.8.1 USING THE TANH-COTH METHOD 593 14.8.2 IV-SOLITON SOLUTIONS OF THE
HIROTA-SATSUMA SYSTEM 594 14.8.3 N-SOLITON SOLUTIONS BY AN ALTERNATIVE
METHOD 596 14.9 GENERALIZED SHORT WAVE EQUATION 597 REFERENCES 602 15
FAMILY OF KDV-TYPE EQUATIONS 605 15. CONTENTS XVII 15.6 THE
KADOMTSEV-PETVIASHVILI (KP) EQUATION 620 15.6.1 USING THE TANH-COTH
METHOD 621 15.6.2 MULTIPLE-SOLITON SOLUTIONS OF THE KP EQUATION 622 15.7
THE ZAKHAROV-KUZNETSOV (ZK) EQUATION 626 15.8 THE BENJAMIN-ONO EQUATION
629 15.9 THE KDV-BURGERS EQUATION 630 15.10 SEVENTH-ORDER KDV EQUATION
632 15.10.1 THE SECH METHOD 632 15.11 NINTH-ORDER KDV EQUATION 634
15.11.1 THE SECH METHOD 634 REFERENCES 637 16 BOUSSINESQ, KLEIN-GORDON
AND LIOUVILLE EQUATIONS 639 16.1 INTRODUCTION 639 16.2 THE BOUSSINESQ
EQUATION 641 16.2.1 USING THE TANH-COTH METHOD 641 16.2.2
MULTIPLE-SOLITON SOLUTIONS OF THE BOUSSINESQ EQUATION. 643 16.3 THE
IMPROVED BOUSSINESQ EQUATION 646 16.4 THE KLEIN-GORDON EQUATION 648 16.5
THE LIOUVILLE EQUATION 649 16.6 THE SINE-GORDON EQUATION 651 16.6.1
USING THE TANH-COTH METHOD 651 16.6.2 USING THE BACKHAND TRANSFORMATION
654 16.6.3 MULTIPLE-SOLITON SOLUTIONS FOR SINE-GORDON EQUATION. 655
16.7 THE SINH-GORDON EQUATION 657 16.8 THE DODD-BULLOUGH-MIKHAILOV
EQUATION 658 16.9 THE TZITZEICA-DODD-BULLOUGH EQUATION 659 16.10 THE
ZHIBER-SHABAT EQUATION 661 REFERENCES 662 17 BURGERS, FISHER AND RELATED
EQUATIONS 665 17.1 INTRODUCTION 665 17.2 THE BURGERS EQUATION 666 17.2.1
USING THE TANH-COTH METHOD 667 17.2.2 USING THE COLE-HOPF TRANSFORMATION
668 17. XVIII CONTENTS 18 FAMILIES OF CAMASSA-HOLM AND SCHRODINGER
EQUATIONS 683 18.1 INTRODUCTION 683 18.2 THE FAMILY OF CAMASSA-HOLM
EQUATIONS 686 18.2.1 USING THE TANH-COTH METHOD 686 18.2.2 USING AN
EXPONENTIAL ALGORITHM 688 18.3 SCHRODINGER EQUATION OF CUBIC
NONLINEARITY 689 18.4 SCHRODINGER EQUATION WITH POWER LAW NONLINEARITY
690 18.5 THE GINZBURG-LANDAU EQUATION 692 18.5.1 THE CUBIC
GINZBURG-LANDAU EQUATION 693 18.5.2 THE GENERALIZED CUBIC
GINZBURG-LANDAU EQUATION 694 18.5.3 THE GENERALIZED QUINTIC
GINZBURG-LANDAU EQUATION . 695 REFERENCES 696 APPENDIX 699 A
INDEFINITE INTEGRALS 699 A.1 FUNDAMENTAL FORMS 699 A.2 TRIGONOMETRIC
FORMS 700 A.3 INVERSE TRIGONOMETRIC FORMS 700 A.4 EXPONENTIAL AND
LOGARITHMIC FORMS 701 A.5 HYPERBOLIC FORMS 701 A.6 OTHER FORMS 702 B
SERIES 703 B.I EXPONENTIAL FUNCTIONS 703 B.2 TRIGONOMETRIC FUNCTIONS 703
B.3 INVERSE TRIGONOMETRIC FUNCTIONS 704 B.4 HYPERBOLIC FUNCTIONS 704 B.5
INVERSE HYPERBOLIC FUNCTIONS 704 C EXACT SOLUTIONS OF BURGERS' EQUATION
705 D PADE APPROXIMANTS FOR WELL-KNOWN FUNCTIONS 707 D. 1 EXPONENTIAL
FUNCTIONS 707 D.2 TRIGONOMETRIC FUNCTIONS 707 D.3 HYPERBOLIC FUNCTIONS
709 D. CONTENTS XIX F INFINITE SERIES 712 F.I NUMERICAL SERIES 712 F.2
TRIGONOMETRIC SERIES 713 ANSWERS 715 INDEX 739 |
| any_adam_object | 1 |
| author | Wazwaz, Abdul-Majid |
| author_GND | (DE-588)1076753868 |
| author_facet | Wazwaz, Abdul-Majid |
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| author_sort | Wazwaz, Abdul-Majid |
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| building | Verbundindex |
| bvnumber | BV035808330 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
| callnumber-search | QA377 |
| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 SK 950 |
| ctrlnum | (OCoLC)310400928 (DE-599)DNB992291526 |
| dewey-full | 515.353 530.155353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 530 - Physics |
| dewey-raw | 515.353 530.155353 |
| dewey-search | 515.353 530.155353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV035808330 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T06:44:21Z |
| institution | BVB |
| isbn | 9787040254808 9783642002502 |
| language | English |
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| open_access_boolean | |
| owner | DE-703 DE-83 DE-11 |
| owner_facet | DE-703 DE-83 DE-11 |
| physical | XIX, 741 S. graph. Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Higher Education Press Springer |
| record_format | marc |
| series2 | Nonlinear physical science |
| spelling | Wazwaz, Abdul-Majid Verfasser (DE-588)1076753868 aut Partial differential equations and solitary waves theory Abdul-Majid Wazwaz Beijing Higher Education Press 2009 Berlin [u.a.] Springer XIX, 741 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Nonlinear physical science Literaturangaben Partielle Differentialgleichung Soliton Differential equations, Partial Wave equation Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Soliton (DE-588)4135213-0 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 Soliton (DE-588)4135213-0 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018667299&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wazwaz, Abdul-Majid Partial differential equations and solitary waves theory Partielle Differentialgleichung Soliton Differential equations, Partial Wave equation Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Soliton (DE-588)4135213-0 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4135213-0 |
| title | Partial differential equations and solitary waves theory |
| title_auth | Partial differential equations and solitary waves theory |
| title_exact_search | Partial differential equations and solitary waves theory |
| title_full | Partial differential equations and solitary waves theory Abdul-Majid Wazwaz |
| title_fullStr | Partial differential equations and solitary waves theory Abdul-Majid Wazwaz |
| title_full_unstemmed | Partial differential equations and solitary waves theory Abdul-Majid Wazwaz |
| title_short | Partial differential equations and solitary waves theory |
| title_sort | partial differential equations and solitary waves theory |
| topic | Partielle Differentialgleichung Soliton Differential equations, Partial Wave equation Numerical solutions Partielle Differentialgleichung (DE-588)4044779-0 gnd Soliton (DE-588)4135213-0 gnd |
| topic_facet | Partielle Differentialgleichung Soliton Differential equations, Partial Wave equation Numerical solutions |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018667299&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT wazwazabdulmajid partialdifferentialequationsandsolitarywavestheory |