[HTML][HTML] New findings for the old problem: Exact solutions for domain walls in coupled real Ginzburg-Landau equations
BA Malomed - Physics Letters A, 2022 - Elsevier
This work reports new exact solutions for domain-wall (DW) states produced by a system of
coupled real Ginzburg-Landau (GL) equations which model patterns in thermal convection …
coupled real Ginzburg-Landau (GL) equations which model patterns in thermal convection …
Past and present trends in the development of the pattern-formation theory: domain walls and quasicrystals
BA Malomed - Physics, 2021 - mdpi.com
A condensed review is presented for two basic topics in the theory of pattern formation in
nonlinear dissipative media:(i) domain walls (DWs, alias grain boundaries), which appear as …
nonlinear dissipative media:(i) domain walls (DWs, alias grain boundaries), which appear as …
Domain walls and vector solitons in the coupled nonlinear Schrödinger equation
We outline a program to classify domain walls (DWs) and vector solitons in the 1D two-
component coupled nonlinear Schrödinger (CNLS) equation without restricting the signs or …
component coupled nonlinear Schrödinger (CNLS) equation without restricting the signs or …
Interface layer of a two-component Bose–Einstein condensate
A Aftalion, C Sourdis - Communications in Contemporary …, 2017 - World Scientific
This paper deals with the study of the behavior of the wave functions of a two-component
Bose–Einstein condensate near the interface, in the case of strong segregation. This yields …
Bose–Einstein condensate near the interface, in the case of strong segregation. This yields …
The heteroclinic connection problem for general double-well potentials
C Sourdis - Mediterranean Journal of Mathematics, 2016 - Springer
The Heteroclinic Connection Problem for General Double-Well Potentials Page 1 Mediterr. J.
Math. 13 (2016), 4693–4710 DOI 10.1007/s00009-016-0770-0 1660-5446/16/064693-18 …
Math. 13 (2016), 4693–4710 DOI 10.1007/s00009-016-0770-0 1660-5446/16/064693-18 …
Monotonicity and rigidity of solutions to some elliptic systems with uniform limits
Monotonicity and rigidity of solutions to some elliptic systems with uniform limits Page 1
Communications in Contemporary Mathematics Vol. 22, No. 5 (2020) 1950044 (24 pages) c© …
Communications in Contemporary Mathematics Vol. 22, No. 5 (2020) 1950044 (24 pages) c© …
Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system
P Le - Fractional Calculus and Applied Analysis, 2023 - Springer
We prove the monotonicity and one-dimensional symmetry of solutions to non-cooperative
fractional elliptic systems with uniform limits. In particular, our result holds for phase …
fractional elliptic systems with uniform limits. In particular, our result holds for phase …
Stability of black solitons in optical systems with intensity-dependent dispersion
DE Pelinovsky, M Plum - SIAM Journal on Mathematical Analysis, 2024 - SIAM
Black solitons are identical in the nonlinear Schrödinger (NLS) equation with intensity-
dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity …
dependent dispersion and the cubic defocusing NLS equation. We prove that the intensity …
Phase segregation for binary mixtures of Bose--Einstein condensates
We study the strong segregation limit for mixtures of Bose--Einstein condensates modeled
by a Gross--Pitaevskii functional. Our first main result is that in the presence of a trapping …
by a Gross--Pitaevskii functional. Our first main result is that in the presence of a trapping …
Pinning in the extended Lugiato–Lefever equation
We consider a variant of the Lugiato–Lefever equation (LLE), which is a nonlinear
Schrödinger equation on a one-dimensional torus with forcing and damping, to which we …
Schrödinger equation on a one-dimensional torus with forcing and damping, to which we …