The “good” Boussinesq equation : long-time asymptotics [PDF]
Analysis & PDE, 2020 We consider the initial-value problem for the ``good'' Boussinesq equation on the line. Using inverse scattering techniques, the solution can be expressed in terms of the solution of a $3 \times 3$-matrix Riemann-Hilbert problem.
C. Charlier, J. Lenells, D. Wang
semanticscholar +7 more sources
Long-Time Asymptotics of a Three-Component Coupled mKdV System
Mathematics, 2019 We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated.
Wen-Xiu Ma, Ma Wen-Xiu
exaly +4 more sources
Long-Time Asymptotics for the Nonlocal MKdV Equation [PDF]
Communications in Theoretical Physics, 2018 In this paper, we study the Cauchy problem with decaying initial data for the nonlocal modified Korteweg-de Vries equation (nonlocal mKdV) \[q_t(x,t)+q_{xxx}(x,t)-6q(x,t)q(-x,-t)q_x(x,t)=0,\] which can be viewed as a generalization of the local ...
F. He, E. Fan, Jian Xu
semanticscholar +5 more sources
Long-time asymptotics for an integrable evolution equation with a $3 \times 3$ Lax pair [PDF]
, 2021 We derive a Riemann--Hilbert representation for the solution of an integrable nonlinear evolution equation with a $3 \times 3$ Lax pair. We use the derived representation to obtain formulas for the long-time asymptotics.
C. Charlier, J. Lenells
semanticscholar +3 more sources
Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data
Journal of Differential Equations, 2021 We study the Cauchy problem for the integrable nonlocal nonlinear Schrodinger (NNLS) equation i q t ( x , t ) + q x x ( x , t ) + 2 q 2 ( x , t ) q ¯ ( − x , t ) = 0 with a step-like initial data: q ( x , 0 ) = q 0 ( x ) , where q 0 ( x ) = o ( 1 ) as x →
Yan Rybalko, Dmitry Shepelsky
exaly +2 more sources
On the Cauchy problem of defocusing mKdV equation with finite density initial data: Long time asymptotics in soliton-less regions [PDF]
Journal of Differential Equations, 2021 We investigate the long-time asymptotics for the solutions to the Cauchy problem of defocusing modified Kortweg-de Vries (mKdV) equation with finite density initial data.
Taiyang Xu, Zechuan Zhang, E. Fan
semanticscholar +4 more sources
Long-Time Asymptotics of A Perturbed Modified KdV Equation
Journal of Nonlinear ScienceWe derive full asymptotics of the modified KdV equation (mKdV) with a higher-order perturbative term. We make use of the perturbative theory of infinite-dimensional integrable systems developed by P. Deift and X. Zhou \cite{DZ-2}, and some new and simpler proofs of certain $L^\infty$ bounds and $L^p$ a priori estimates developed recently in \cite{CLT}.
Gong Chen, Jiaqi Liu, Yuanhong Tian
semanticscholar +3 more sources
Semidiscretization and Long-time Asymptotics of Nonlinear Diffusion Equations [PDF]
Communications in Mathematical Sciences, 2007 We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed.
CARRILLO J. A +2 more
core +7 more sources
The Deift–Zhou steepest descent method to long-time asymptotics for the Sasa–Satsuma equation
Journal of Differential Equations, 2018 The initial value problem for the Sasa–Satsuma equation is transformed to a 3 × 3 matrix Riemann–Hilbert problem with the help of the corresponding Lax pair. Two distinct factorizations of the jump matrix and a decomposition of the vector-valued function
Bo Xue, Xianguo Geng
exaly +2 more sources
Existence of weak solutions and long‐time asymptotics for hydrodynamic model of swarming [PDF]
Journal of the London Mathematical SocietyWe consider a one‐dimensional hydrodynamic model featuring nonlocal attraction–repulsion interactions and singular velocity alignment. We introduce a two‐velocity reformulation and the corresponding energy‐type inequality, in the spirit of the Bresch ...
N. Chaudhuri +3 more
semanticscholar +6 more sources