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Multiple soliton solutions and other exact solutions for a two‐mode KdV equation
Author(s) -
Wazwaz AbdulMajid
Publication year - 2017
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.4138
Subject(s) - korteweg–de vries equation , mathematics , soliton , hyperbolic function , work (physics) , dispersion (optics) , mathematical analysis , nonlinear system , mode (computer interface) , traveling wave , mathematical physics , physics , quantum mechanics , computer science , operating system
In this work, we study the two‐mode Korteweg–de Vries (TKdV) equation, which describes the propagation of two different waves modes simultaneously. We show that the TKdV equation gives multiple soliton solutions for specific values of the nonlinearity and dispersion parameters involved in the equation. We also derive other distinct exact solutions for general values of these parameters. We apply the simplified Hirota's method to study the specific of the parameters, which gives multiple soliton solutions. We also use the tanh/coth method and the tan/cot method to obtain other set of solutions with distinct physical structures. Copyright © 2016 John Wiley & Sons, Ltd.