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2016•Advances in Difference EquationsOpen access

Quasi-periodic wave solutions and asymptotic behavior for an extended ( 2 + 1 ) $(2+1)$ -dimensional shallow water wave equation

Wenjuan Rui

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Abstract

Based on Riemann theta function and bilinear Bäcklund transformation, quasi-periodic wave solutions are constructed for an extended $(2+1)$ -dimensional shallow water wave equation. A detail asymptotic analysis procedure to the one- and two-periodic wave solutions are presented, and the asymptotic properties of this type of solutions are proved. It is shown that the quasi-periodic wave solutions converge to the soliton solutions under small amplitude limits.

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Based on Riemann theta function and bilinear Bäcklund transformation, quasi-periodic wave solutions are constructed for an extended $(2+1)$ -dimensional shallow water wave equation. A detail asymptotic analysis procedure to the one- and two-periodic wave solutions are presented, and the asymptotic properties of this type of solutions are proved. It is shown that the quasi-periodic wave solutions converge to the soliton solutions under small amplitude limits.

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Available abstract

Based on Riemann theta function and bilinear Bäcklund transformation, quasi-periodic wave solutions are constructed for an extended $(2+1)$ -dimensional shallow water wave equation. A detail asymptotic analysis procedure to the one- and two-periodic wave solutions are presented, and the asymptotic properties of this type of solutions are proved. It is shown that the quasi-periodic wave solutions converge to the soliton solutions under small amplitude limits.

Key concepts: Mathematics, Mathematical analysis, Riemann hypothesis, Periodic wave, Waves and shallow water, Partial differential equation, Transformation (genetics), Soliton

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