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Zbl 1229.35232
Triki, Houria; Wazwaz, Abdul-Majid
Bright and dark soliton solutions for a $K(m,n)$ equation with $t$-dependent coefficients. (English)
[J] Phys. Lett., A 373, No. 25, 2162-2165 (2009). ISSN 0375-9601

Summary: The propagation of soliton pulses in an inhomogeneous media that is described by a $K(m,n)$ equation with $t$-dependent coefficients is studied. By using a solitary wave ansatz in the form of $\text{sech}^{(p)}$ and $\text{tanh}^{(p)}$ functions, respectively, we obtain the exact bright and dark soliton solutions for the considered model. All the physical parameters in the solitary wave solutions are obtained as functions of the varying model coefficients. Such solutions may be useful to explain the dynamics of wave propagation in nonlinear $K(m,n)$ systems exhibiting varying dispersive and nonlinear effects. Parametric conditions for the formation of soliton pulses are determined.

MSC 2000:: *35Q51 Solitons
35Q41
35C08
37K10 Completely integrable systems etc.

Keywords: bright and dark soliton solution; variable-coefficient $K(m,n)$ equation; sech and tanh ansatzes

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