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Math. Comput. Appl. 2015, 20(1), 50-61; doi:10.3390/mca20010061

Homotopic Approximate Solutions for the General Perturbed Nonlinear Schrödinger Equation

1
Department of Mathematical and Physical Science, Nanjing Institute of Technology, Nanjing 211167, China
2
Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu, 212013, China
*
Authors to whom correspondence should be addressed.
Published: 1 April 2015
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Abstract

In this work, a class of perturbed nonlinear Schrödinger equation is studied by using the homotopy perturbation method. Firstly, we obtain some Jacobi-like elliptic function solutions of the corresponding typical general undisturbed nonlinear Schrödinger equation through the mapping deformation method, and secondly, a homotopic mapping transform is constructed, then the approximate solution with arbitrary degree of accuracy for the perturbed equation is researched, it is pointed out that the series of approximate solution is convergent. Finally, the efficiency and accuracy of the approximate solution is also discussed by using the fixed point theorem.
Keywords: perturbed nonlinear Schrödinger equation; homotopic mapping; asymptotic method; approximate solution perturbed nonlinear Schrödinger equation; homotopic mapping; asymptotic method; approximate solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hong, B.; Lu, D.; Liu, Y. Homotopic Approximate Solutions for the General Perturbed Nonlinear Schrödinger Equation. Math. Comput. Appl. 2015, 20, 50-61.

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