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A new symmetry approach to solve space–time‐dependent KdV systems
Author(s) -
Ruan Hangyu,
Chen Yixin
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.445
Subject(s) - korteweg–de vries equation , mathematics , soliton , variable (mathematics) , space (punctuation) , symmetry (geometry) , variable coefficient , mathematical analysis , nonlinear system , geometry , computer science , physics , quantum mechanics , operating system
In this paper, a new method to solve space–time‐dependent non‐linear equations is proposed. After considering the variable coefficient of a non‐linear equation as a new dependent variable, some special types of space–time‐dependent equations can be solved from corresponding space–time‐independent equations by using the general classical Lie approach. The rich soliton solutions of space–time‐dependent KdV equation and mKdV equation are given with the help of the approach. Copyright © 2004 John Wiley & Sons, Ltd.