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首页> 外文期刊>Romanian journal of physics >Travelling Wave Solutions for the Long-Short Wave Resonance Model through an Improved (G'/G) -Expansion Method
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Travelling Wave Solutions for the Long-Short Wave Resonance Model through an Improved (G'/G) -Expansion Method

机译：通过改进的（G'/ G）扩展方法对长短波共​​振模型的行波解

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In this paper the long-short ( LS ) wave resonance model is investigated. An efficient approach, able to classify the types of solutions according to the values of some parameters, is provided. The solutions of the ( LS ) system are presented as polynomial expansions in two variables which do satisfy the projective Riccati equations, but without asking for their explicit solutions. The key feature is to take a full advantage of a well known and simpler ODE. The Lie symmetry method is as well taken into consideration since it leads to supplementary solutions. We pointed out solutions such as ( a ) solitary wave solution of bell-type, ( b ) solitary wave solution of kink-type for S and bell-type for L , ( c ) solitary wave solution of a compound of the bell-type and the kink-type for S and L , ( d ) singular travelling wave solutions and ( e ) solitary wave solution of rational function type. The concerned method can as well be used in order to study other interesting nonlinear evolution processes in n dimensions.
机译：本文研究了长短（LS）共振模型。提供了一种有效的方法，能够根据某些参数的值对解决方案的类型进行分类。 （LS）系统的解表示为两个变量的多项式展开式，这些变量确实满足射影Riccati方程，但不要求其显式解。关键功能是充分利用众所周知且更简单的ODE。 Lie对称方法也得到了考虑，因为它导致了补充解。我们指出了以下解决方案，例如：（a）钟型孤波解，（b）S的扭结型孤波解和L的钟型，（c）钟型化合物的孤波解以及S和L的扭结类型，（d）奇异行波解和（e）有理函数类型的孤波解。还可以使用所关注的方法来研究n维中其他有趣的非线性演化过程。

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