## AIMS Lab Seminar - Tao Xu - Soliton solutions of the Sasa-Satsuma equation in the modulation stable region

- Calendar
- Mathematics & Statistics

- Date
- 11.18.2019 11:30 am - 12:20 pm

### Description

HH 403

Speaker: Tao Xu

Title: Soliton solutions of the Sasa-Satsuma equation in the modulation stable region

Abstract: The Sasa-Satsuma equation is an integrable higher-order generalization of the NLS equation which admits the 3*3 Lax pair. By the one-fold Darboux transformation, we construct the exponential, algebraic, mixed soliton solutions in the modulation stable region. With proper degenerate conditions, we obtain the single solitons including the exponential anti-dark and Mexican-hat (MH) solitons, as well as the algebraic MH solitons. For the generic cases, we study the asymptotic behavior of three types of soliton solutions. As a result, we reveal the resonant interactions among three exponential solitons, the annihilation and creation of the algebraic MH soliton pair, and the non-resonant interactions among one algebraic soliton and two mixed solitons. The asymptotic analysis technique is developed in studying the algebraic and mixed soliton solutions, so that we derive the asymptotic solitons with the algebraic or logarithmic center trajectory.

Speaker: Tao Xu

Title: Soliton solutions of the Sasa-Satsuma equation in the modulation stable region

Abstract: The Sasa-Satsuma equation is an integrable higher-order generalization of the NLS equation which admits the 3*3 Lax pair. By the one-fold Darboux transformation, we construct the exponential, algebraic, mixed soliton solutions in the modulation stable region. With proper degenerate conditions, we obtain the single solitons including the exponential anti-dark and Mexican-hat (MH) solitons, as well as the algebraic MH solitons. For the generic cases, we study the asymptotic behavior of three types of soliton solutions. As a result, we reveal the resonant interactions among three exponential solitons, the annihilation and creation of the algebraic MH soliton pair, and the non-resonant interactions among one algebraic soliton and two mixed solitons. The asymptotic analysis technique is developed in studying the algebraic and mixed soliton solutions, so that we derive the asymptotic solitons with the algebraic or logarithmic center trajectory.

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