this paper aims to study a generalized double sinh-gordon equation, which appears in several physical phenomena such as integrable quantum field theory, kink dynamics and fluid dynamics. lie symmetry analysis together with the simplest equation method is used to obtain exact solutions for this equation. moreover, we derive conservation laws for the equation by using two different approaches, na...

In this paper, dependent and independent variable transformations are introduced to solve a generalized sinh–Gordon equation by using the binary F-expansion method and the knowledge of elliptic equation and Jacobian elliptic functions. Many different new exact solutions such as double periodic wave and complex wave solutions are obtained. Some previous results are extended. 2013 Elsevier Inc. A...

In this work, we successfully construct the new exact traveling wave solutions of the generalized Sinh–Gordon equation by new application of the homogeneous balance method. The idea introduced in this paper can be applied to other nonlinear evolution equations.

in this work, we successfully construct the new exact traveling wave solutions ofthe generalized sinh–gordon equation by new application of the homogeneousbalance method. the idea introduced in this paper can be applied to othernonlinear evolution equations.

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two P(φ)2 systems with polynomial self-interactions.

In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.

In this paper we derive some exact solutions for the Ito equation. These solutions are obtained by the sn-ns method, which is a generalization of the tanh-coth method.

Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

In this paper, the (G′/G)-expansion method is applied to seek traveling wave solutions of the combined and the double combined sinh-cosh-Gordon equations. This traveling wave solutions are expressed by the hyperbolic functions and the trigonometric functions. It is shown that the proposed method is direct, effective and more general. 2000 Mathematics Subject Classification: 35K01; 35J05.