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Solitary wave solutions for a generalized KdV–mKdV equation with variable coefficients

✍ Scribed by Houria Triki; Thiab R. Taha; Abdul-Majid Wazwaz

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
126 KB
Volume
80
Category
Article
ISSN
0378-4754

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✦ Synopsis

In this work, a generalized time-dependent variable coefficients combined KdV-mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type solitary waves, kink type solitary waves, and combined type solitary waves solutions for the considered model. Importantly, the results show that there exist combined solitary wave solutions in inhomogeneous KdV-typed systems, after proving their existence in the nonlinear Schrödinger systems. It should be noted that, the characteristics of the obtained solitary wave solutions have been expressed in terms of the time-dependent coefficients. Moreover, we give the formation conditions of the obtained solutions for the considered KdV-mKdV equation with variable coefficients.

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