Conservation laws of the complex short pulse equation and coupled complex short pulse equations |
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Authors: | Lihua Zhang Bo Shen Shuxin Han Gangwei Wang Lingshu Wang |
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Institution: | School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China |
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Abstract: | In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated. |
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Keywords: | complex short pulse equation coupled complex short pulse equations symmetries adjoint symmetries conservation laws SA method |
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