Analysis of stability and instability for standing waves of the double power one dimensional nonlinear Schrödinger equation

[1]  Ian Zwiers,et al.  Existence and stability of standing waves for one dimensional NLS with triple power nonlinearities , 2021, 2102.01246.

[2]  Phan Van Tin.  On the derivative nonlinear Schrödinger equation on the half line with Robin boundary condition , 2021, 2102.00727.

[3]  Mathieu Lewin,et al.  The double-power nonlinear Schrödinger equation and its generalizations: uniqueness, non-degeneracy and applications , 2020, Calculus of Variations and Partial Differential Equations.

[4]  M. Hayashi,et al.  Instability of algebraic standing waves for nonlinear Schrödinger equations with double power nonlinearities , 2020, Transactions of the American Mathematical Society.

[5]  J. Pava,et al.  Orbital stability of standing waves for the nonlinear Schrödinger equation with attractive delta potential and double power repulsive nonlinearity , 2019, Journal of Mathematical Physics.

[6]  César A. Hernández Melo,et al.  On stability properties of the Cubic-Quintic Schródinger equation with \begin{document}$\delta$\end{document}-point interaction , 2019, Communications on Pure & Applied Analysis.

[7]  Yifei Wu,et al.  Instability of the solitary wave solutions for the generalized derivative nonlinear Schrödinger equation in the critical frequency case , 2018, Mathematical Research Letters.

[8]  Stefan Le Coz,et al.  Stability of Multisolitons for the Derivative Nonlinear Schrödinger Equation , 2017 .

[9]  S. Nodari,et al.  Orbital Stability via the Energy–Momentum Method: The Case of Higher Dimensional Symmetry Groups , 2016, 1605.02523.

[10]  B. Malomed,et al.  Stable NLS solitons in a cubic-quintic medium with a delta-function potential , 2014, 1409.6511.

[11]  S. Nodari,et al.  Orbital Stability: Analysis Meets Geometry , 2014, 1407.5951.

[12]  Masahito Ohta,et al.  Strong instability of standing waves for nonlinear Schr\"odinger equations with double power nonlinearity , 2014, 1407.0905.

[13]  Stefan Le Coz,et al.  Minimal mass blow up solutions for a double power nonlinear Schr\"odinger equation , 2014, 1406.6002.

[14]  Christophe Besse,et al.  Communi-cations Computational methods for the dynamics of the nonlinear Schr̈odinger / Gross-Pitaevskii equations , 2013 .

[15]  Masaya Maeda.  Stability of bound states of Hamiltonian PDEs in the degenerate cases , 2011, 1107.3629.

[16]  Masahito Ohta,et al.  Instability of bound states for abstract nonlinear Schr , 2010, 1010.1511.

[17]  Masaya Maeda.  Stability and instability of standing waves for 1-dimensional nonlinear Schrödinger equation with multiple-power nonlinearity , 2008 .

[18]  Christophe Besse,et al.  A Relaxation Scheme for the Nonlinear Schrödinger Equation , 2004, SIAM J. Numer. Anal..

[19]  Dmitry E. Pelinovsky,et al.  Purely nonlinear instability of standing waves with minimal energy , 2003 .

[20]  A Ankiewicz,et al.  Hamiltonian-versus-energy diagrams in soliton theory. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Masahito Ohta.  Stability of standing waves for the generalized Davey-Stewartson system , 1994, Differential and Integral Equations.

[22]  I. Iliev,et al.  Stability and instability of solitary waves for one-dimensional singular Schrödinger equations , 1993, Differential and Integral Equations.

[23]  Nakao Hayashi,et al.  On the derivative nonlinear Schro¨dinger equation , 1992 .

[24]  J. Shatah,et al.  Stability theory of solitary waves in the presence of symmetry, II☆ , 1990 .

[25]  Michael I. Weinstein,et al.  Modulational Stability of Ground States of Nonlinear Schrödinger Equations , 1985 .

[26]  M. Weinstein.  Nonlinear Schrödinger equations and sharp interpolation estimates , 1983 .

[27]  Pierre-Louis Lions,et al.  Nonlinear scalar field equations, I existence of a ground state , 1983 .

[28]  P. Lions,et al.  Orbital stability of standing waves for some nonlinear Schrödinger equations , 1982 .