Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations

2001 ◽  
Vol 157 (3) ◽  
pp. 219-254 ◽  
Author(s):  
Yvan Martel ◽  
Frank Merle
Keyword(s):  
Asymptotic Stability ◽  
Kdv Equations ◽  
Generalized Kdv Equations

scholarly journals N-soliton solutions and the Hirota conditions in (1 + 1)-dimensions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Common Factors ◽  
Soliton Solutions ◽  
Higher Order ◽  
Kdv Equations ◽  
The Common ◽  
Bilinear Formulation ◽  
Generalized Kdv Equations ◽  
Hirota Bilinear

Abstract We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.

TRAVELING WAVE SOLUTIONS OF SEVENTH-ORDER GENERALIZED KdV EQUATIONS BY VARIATIONAL ITERATION METHOD USING ADOMIAN'S POLYNOMIALS

2009 ◽  
Vol 23 (15) ◽  
pp. 3265-3277 ◽  
Author(s):  
SYED TAUSEEF MOHYUD-DIN ◽  
MUHAMMAD ASLAM NOOR ◽  
KHALIDA INAYAT NOOR
Keyword(s):  
Applied Sciences ◽  
Iteration Method ◽  
Traveling Wave Solutions ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Seventh Order ◽  
Generalized Kdv Equations ◽  
Adomian’S Polynomials

In this paper, we apply the variational iteration method using Adomian's polynomials (VIMAP) to investigate propagating traveling solitary wave solutions of seventh-order generalized KdV (SOG-KdV) equations, which play a very important role in mathematical physics, engineering, and applied sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, perturbation, linearization, or restrictive assumptions and is formulated by the elegant coupling of variational iteration method and Adomian's polynomials.

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