Nonlinear Evolution Equations for Second-order Spectral Problem

Wei Liu1; Shujuan Yuan2; Shuhong Wang3

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Nonlinear Evolution Equations for Second-order Spectral Problem

机译：二阶光谱问题的非线性演化方程

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—Soliton equations are infinite-dimensional integrable systems described by nonlinear evolution equations. As one of the soliton equations, long wave equation takes on profound significance of theory and reality. By using the method of nonlinearization, the relation between long wave equation and second-order eigenvalue problem is generated. Based on the nonlinearized Lax pairs, Euler-Lagrange function and Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the Bargmann constrained condition between the potential function and the eigenfunction, the Lax pairs is equivalent to matrix spectral problem. Furthermore, the involutive representations of the solutions for long wave equation are generated.

机译：-Soliton方程是非线性演化方程描述的无限尺寸可积系统。作为孤子方程之一，长波方程具有理论和现实的深刻意义。通过使用非线性化方法，产生长波方程与二阶特征值问题之间的关系。基于非线化lex对，欧拉拉格朗函数和legendre转换，获得了合理的jacobi-ostrogradsky坐标系。此外，借助于潜在功能和特征函数之间的Bargmann受限状态，LAX对等同于矩阵光谱问题。此外，生成了长波方程解的涉及表示。

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《Journal of Computers》 |2012年第9期|共8页
作者
Wei Liu1; Shujuan Yuan2; Shuhong Wang3;
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Nonlinear Evolution Equations for Second-order Spectral Problem

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