Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schrödinger's equation with Kerr law nonlinearity |
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Authors: | Zai-yun Zhang Zhen-hai LiuXiu-jin Miao Yue-zhong Chen |
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Institution: | a School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, Hunan, PR China b School of Mathematics and Computer Science, Guangxi University for Nationalities, Nanning 530006, Guangxi, PR China |
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Abstract: | In this Letter, we investigate the perturbed nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution. |
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Keywords: | NLSE with Kerr law nonlinearity Qualitative analysis Traveling wave solutions The bifurcation method Energy level |
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