Soliton Like-Breather Induced by Modulational Instability in a Generalized Nonlinear Schrödinger Equation
We consider the nonlinear Schrödinger equation modified by a rational nonlinear term. The model appears in various studies often in the context of the Ginzburg-Landau equation. We investigate modulational instability by means of a linear stability analysis and show how the nonlinear terms affect the...
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| Main Authors: | , |
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| Format: | Book Chapter |
| Language: | English |
| Published: |
IntechOpen
2021
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| Subjects: | |
| Online Access: | https://www.intechopen.com/chapters/79127 |
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| Summary: | We consider the nonlinear Schrödinger equation modified by a rational nonlinear term. The model appears in various studies often in the context of the Ginzburg-Landau equation. We investigate modulational instability by means of a linear stability analysis and show how the nonlinear terms affect the growth rate. This analytical result is confirmed by a numerical simulation. The latter analysis shows that breather-like solitons are generated from the instability, and the effects of the nonlinear terms are again clearly seen. Moreover, by employing an auxiliary-equation method we obtain kink and anti-kink soliton as analytical solutions. Our theoretical solution is in good agreement with our numerical investigation. |
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| ISBN: | 978-1-83969-978-8 |
| DOI: | 10.5772/intechopen.100522 |