Orbital stability of solitary waves for the generalized long-short wave resonance equations with a cubic-quintic strong nonlinear term

被引：4

作者：

Zheng, Xiaoxiao ^{[1
]}

Di, Huafei ^{[2
]}

Peng, Xiaoming ^{[3
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273155, Shandong, Peoples R China

[2] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China

[3] Guangdong Univ Finance & Econ, Sch Stat & Math, Guangzhou 510320, Guangdong, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2020年 / 2020卷 / 01期

关键词：

Long-short resonance wave equations; Cubic-quintic nonlinearity; Solitary waves; Orbital stability; TIME BEHAVIOR; GLOBAL SOLUTION; EXISTENCE;

D O I：

10.1186/s13660-020-02505-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the orbital stability of solitary waves for the following generalized long-short wave resonance equations of Hamiltonian form: {iu(t) + u(xx) = alpha uv + gamma vertical bar u|vertical bar(2)u + delta|u vertical bar(4)u, v(t) + beta vertical bar u vertical bar(2)(x) = 0. We first obtain explicit exact solitary waves for Eqs. (0.1). Second, by applying the extended version of the classical orbital stability theory presented by Grillakis et al., the approach proposed by Bona et al., and spectral analysis, we obtain general results to judge orbital stability of solitary waves. We finally discuss the explicit expression of det(d '') in three cases and provide specific orbital stability results for solitary waves. Especially, we can get the results obtained by Guo and Chen with parameters alpha=1, beta=-1, and delta=0. Moreover, we can obtain the orbital stability of solitary waves for the classical long-short wave equation with gamma=delta=0 and the orbital instability results for the nonlinear Schrodinger equation with beta = 0.

引用

页数：19