The Simplest Equation Method for Solving Some Important Nonlinear Partial Differential Equations
نویسندگان
چکیده
The simplest equation method presents a wide applicability to handling nonlinear wave equations. In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The simplest equation method is used to construct the travelling wave solutions of new Hamiltonian amplitude equation, (3 + 1)-dimensional generalized KP equation, Burgers-KP equation, coupled Higgs field equation, generalized Zakharov System. New Hamiltonian amplitude equation is an equation which governs certain instabilities of modulated wave trains, with the additional term − uxt overcoming the ill-posedness of the unstable nonlinear Schrödinger equation. It is a Hamiltonian analogue of the Kuramoto-Sivashinski equation which arises in dissipative systems and is apparently not integrable. 2000 Mathematics Subject Classification: 35Q53, 35Q80, 35Q55, 35G25.
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