Results 21 to 30 of about 64 (63)

High order multiscale analysis of discrete integrable equations [PDF]

Open Communications in Nonlinear Mathematical Physics
In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions
Rafael Hernandez Heredero, Decio Levi, Christian Scimiterna   +2 more
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Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation

Advances in Nonlinear Analysis
In this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the
Shan Minjie, Chen Mingjuan, Lu Yufeng, Wang Jing   +3 more
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On an Example of Derivative Nonlinear Schrödinger Equation with D2 Reduction [PDF]

, 2019
[Gerdjikov V. S.; Герджиков В. С.]; [Stefanov A. A.; Stefanov A. Aleksander; Стефанов А.
Stefanov, A. A., Gerdjikov, V. S.
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Bäcklund–Darboux Transformations and Discretizations of Super KdV Equation

, 2014
. For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.
Xue, L.L., Qing Ping Liu, Liu, Q.P., Ling-ling Xue   +3 more
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New Types of Two Component NLS-Type Equations [PDF]

, 2016
[Gerdjikov V. S.; Герджиков В. С.]; [Stefanov A. A.; Stefanov A. Aleksander; Стефанов А.
Stefanov, A. A., Gerdjikov, V. S.
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New Reductions of a Matrix Generalized Heisenberg Ferromagnet Equation [PDF]

, 2018
[Valchev Tihomir; Вълчев Тихомир]; [Yanovski Alexandar; Яновски Александър]In this report, we shall present a new 1 + 1 dimensional nonlinear partial differential equation integrable through inverse scattering transform.
Valchev, Tihomir, Yanovski, Alexandar
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Riemann-Hilbert Problems with Canonical Normalization and Families of Commuting Operators [PDF]

, 2012
2010 Mathematics Subject Classification: 35Q15, 31A25, 37K10, 35Q58.We start with a Riemann-Hilbert Problems (RHP) with canon- ical normalization whose sewing functions depends on several additional vari- ables.
Gerdjikov, V. S.
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Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
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Rogue peakon, posedness and blow-up phenomenon for an integrable Camassa–Holm type equation

Advances in Nonlinear Analysis
In this paper, we study an integrable Camassa–Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon ...
Zhu Mingxuan, Qiao Zhijun, Wang Zhidong, Jiang Zaihong   +3 more
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Integrable system of null curve and Betchov-Da Rios equation

Demonstratio Mathematica
This study focuses on the time evolution of a null curve using a new frame and a new transformation in Minkowski 3-space. Accordingly, Landau–Lifshitz and coupled Boussinesq-like equations for the null curve are provided in terms of the new ...
Yoon Dae Won
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