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The Exact Travelling Wave Solutions for Three Types of Generalized KdV Equations

Author: YinJun
Tutor: LaiShaoYong
School: Sichuan Normal University
Course: Basic mathematics
Keywords: KdV-mKdV equation Generalized KdV Equation Reduction method Auxiliary differential equation Solitary wave solutions Periodic solution Soliton Solutions Algebraic traveling wave solutions Physical Structure
CLC: O175.29
Type: Master's thesis
Year: 2008
Downloads: 73
Quote: 0
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Abstract


In this paper, differential reduction method and auxiliary differential equation method , discussed three types of nonlinear generalized KdV equation traveling wave solutions , some new results are obtained , respectively, led to Xie pointed out changes in the physical structure of the main parameters . Using differential equations reduction Act , Chapter two classes of generalized KdV equation ut (au n -bu 2n ) ux [u k (u < sup> m ) xx ] x = 0 and ut (au n -bu 2n ) ux uk (um) xxx = 0, in different conditions, to obtain the corresponding traveling wave solutions , including solitary wave solutions, soliton solutions , tight soliton solutions , periodic solutions and algebraic traveling wave solutions for the same time, pointed out the nonlinear equation items index nonlinearity coefficient and velocity together to determine changes in the physical structure of solutions of the third chapter, using the auxiliary differential equation method, a class of variable coefficient generalized KdV equation ut α (t) (un) x β (t) (un ) xxx = 0, n gt; 1. through Maple computing , traveling wave solutions obtained analytical expressions to understand that the physical structure of the α (t), β (t) and the exponent n joint decision .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
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