Secular-free solution up to third order of a model nonlinear equation for dispersive waves |
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Authors: | S K Chandra |
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Institution: | 1. Department of Mathematics, Krishna Chandra College, P.O. Hetampur Rajbati, Dist. Birbhum, W. Bengal, India
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Abstract: | The perturbation method of Lindstedt is applied to study the non linear effect of a nonlinear equation $$\nabla ^2 {\rm E} - \frac{1}{{c^2 }}\frac{{\partial ^2 {\rm E}}}{{\partial t^2 }} - \frac{{\omega _0^2 }}{{c^2 }}{\rm E} + \frac{{2v}}{{c^2 }}\frac{{\partial {\rm E}}}{{\partial t}} + E^2 \left {\frac{{\partial {\rm E}}}{{\partial t}} \times A} \right] = 0,$$ where (A. E)=0 andA,c, ω 0 andν are constants in space and time. Amplitude dependent frequency shifts and the solution up to third order are derived. |
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