Periodic traveling waves in the ϕ^{4} model: Instability, stability, and localized structures.
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DOI: 10.1103/physreve.107.034210
Abstract: We consider the instability and stability of periodic stationary solutions to the classical ϕ^{4} equation numerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and the spectrum forms… read more here.
Keywords: periodic traveling; instability; traveling waves; instability stability ... See more keywords
Two-Dimensional Shock Waves for a Model Problem
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DOI: 10.1134/s0001434618050309
Abstract: The existence of nonclassical (two-dimensional) shock waves in Riemann’s problem is proved for a modification of the system of shallow water equations. read more here.
Keywords: waves model; shock waves; two dimensional; dimensional shock ... See more keywords
Explicit exact periodic wave solutions and their limit forms for a long waves-short waves model
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DOI: 10.11948/2017092
Abstract: A long waves-short waves model is studied by using the approach of dynamical systems. The sufficient conditions to guarantee the existence of solitary wave, kink and anti-kink waves, and periodic wave in different regions of… read more here.
Keywords: wave solutions; waves model; long waves; periodic wave ... See more keywords