Results 51 to 60 of about 95 (93)

Soliton equations: admitted solutions and invariances via B\"acklund transformations [PDF]

Open Communications in Nonlinear Mathematical Physics
A couple of applications of B\"acklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evolution equations.
Sandra Carillo, Cornelia Schiebold
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Symmetries and conservation laws of a fifth-order KdV equation with time-dependent coefficients and linear damping

, 2016
Mathematics Subject Classification: 35C07, 35Q53.A fifth-order KdV equation with time-dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations; for ...
Rosa Silva, Rafael de la, Bruzón Gallego, María de los Santos, Gandarias Núñez, María Luz   +2 more
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A Note on the Stability and Instability of Travelling Wave of Korteweg-de Vries Type: The Periodic Case

Revista de Ciencias, 2010
In this paper we adapt the work of M. Grillakis, J. Shatah, and W. Strauss, or J. Bona, P. Souganidis and W. Strauss to the periodic case in spaces having the mean zero property in order to establish the orbital stability/instability of periodic ...
José R Quintero
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Sharp local well-posedness for KP-I equations in the semilinear regime

Forum of Mathematics, Sigma
We show sharp well-posedness with analytic data-to-solution mapping in the semilinear regime for dispersion-generalized KP-I equations on $\mathbb {R}^2$ and $\mathbb {R} \times \mathbb {T}$ .
Shinya Kinoshita, Akansha Sanwal, Robert Schippa   +2 more
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Lie point symmetry, conservation laws and exact power series solutions to the Fujimoto-Watanabe equation

, 2021
In this paper, the Fujimoto-Watanabe equation is studied with the help of the classical Lie point symmetry analysis method. Infinitesimal generators, the entire geometric vector fields and symmetry groups of the Fujimoto-Watanabe equation are given.
Liu, Yu, Dong, Huanhe, Guo, Baoyong, Fang, Yong   +3 more
core  

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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Solution of Burgers' equation via Lie-group analysis

, 2020
An analysis for Burgers' equation is performed via symmetry analysis. We study the Burgers' equation with two cases for the kinematic viscosity. Firstly, with unity kinematic viscosity. Secondly, with time-dependent kinematic viscosity.
Hossam S Hassan, Mina B Abd-El-Malek
core  

Genus two KdV soliton gases and their long-time asymptotics

Forum of Mathematics, Sigma
This paper employs the Riemann-Hilbert problem and nonlinear steepest descent method of Deift-Zhou to provide a comprehensive analysis of the asymptotic behavior of the genus two Korteweg-de Vries soliton gases.
Deng-Shan Wang, Dinghao Zhu, Xiaodong Zhu   +2 more
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Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

Advances in Nonlinear Analysis, 2017
In this paper, we study the following water wave model with a nonlocal viscous term:
Goubet Olivier, Manoubi Imen
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On the existence of bound and ground states for some coupled nonlinear Schrödinger–Korteweg–de Vries equations

Advances in Nonlinear Analysis, 2017
We show the existence of positive bound and ground states for a system of coupled nonlinear Schrödinger–Korteweg–de Vries equations. More precisely, we prove that there exists a positive radially symmetric ground state if either the coupling coefficient ...
Colorado Eduardo
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