A Nonlinear Transformation of the Dispersive Long Wave Equations in (2+1) Dimensions and its Applications
نویسندگان
چکیده
ht + (uh+ u+ uxy)x = 0 (1.2) which were first obtained by Boiti et al [1] as a compatibility condition for a “weak” Lax pair. A Kac-Moody-Virasoro type Lie algebra for eqs. (1.1) and (1.2) were given by Paquin and Winternitz [2]. Moreover, Sen-yue Lou [3] showed that eqs. (1.1) and (1.2) do not pass the Painlevé test, both in the ARS algorithm and in the WTC approach. Equations (1.1) and (1.2) can be reduced to the (1 + 1) dimensional model [4]
منابع مشابه
Comparison Differential Transformation Technique with Adomian Decomposition Method for Dispersive Long-wave Equations in (2+1)-Dimensions
In this paper, we will introduce two methods to obtain the numerical solutions for the system of dispersive long-wave equations (DLWE) in (2+1)-dimensions. The first method is the differential transformation method (DTM) and the second method is Adomian decomposition method (ADM). Moreover, we will make comparison between the solutions obtained by the two methods. Consequently, the results of o...
متن کاملGauge-invariant description of some (2+1)-dimensional integrable nonlinear evolution equations
New manifestly gauge-invariant forms of two-dimensional generalized dispersive long wave and NizhnikVeselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous two-dimensional generalization of dispersive long wave system of equations, Nizhnik-Veselov-Novikov and modified Nizhnik-Veselov-Novikov equations and other known an...
متن کاملAn extended (G′/G)− expansion method and its applications to the (2+1)-dimensional nonlinear evolution equations
By using an extended ( ′ G )-expansion method, we construct the traveling wave solutions of the (2+1)dimensional Painleve integrable Burgers equations, the (2+1)-dimensional Nizhnik-Novikov-Veselov equations, the (2+1)-dimensional Boiti-Leon-Pempinelli equations and the (2+1)-dimensional dispersive long wave equations, where G satisfies the second order linear ordinary differential equation. By...
متن کاملThe B"{a}cklund transformation method of Riccati equation to coupled Higgs field and Hamiltonian amplitude equations
In this paper, we establish new exact solutions for some complex nonlinear wave equations. The B"{a}cklund transformation method of Riccati equation is used to construct exact solutions of the Hamiltonian amplitude equation and the coupled Higgs field equation. This method presents a wide applicability to handling nonlinear wave equations. These equations play a very important role in mathemati...
متن کاملComplexition and solitary wave solutions of the (2+1)-dimensional dispersive long wave equations
In this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. The traveling wave hypothesis yields complexiton solutions. Subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. The constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...
متن کامل