Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential
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DOI: 10.1002/mana.201900427
Abstract: We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the… read more here.
Keywords: class; equations potential; nonlinear schr; inhomogeneous nonlinear ... See more keywords
Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction
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DOI: 10.1002/mana.202400068
Abstract: In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground‐state… read more here.
Keywords: quadratic interaction; system; schr dinger; nonlinear schr ... See more keywords
Traveling waves for a nonlinear Schrödinger system with quadratic interaction in ℝ4$$ {\mathrm{\mathbb{R}}}^4 $$
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DOI: 10.1002/mma.10158
Abstract: In this paper, we consider a nonlinear Schrödinger system with quadratic interaction. We extend the recent results of Fukaya et al. (Math. Ann. 2024) and show that the system has a ground state in ℝ4$$… read more here.
Keywords: system; system quadratic; schr dinger; quadratic interaction ... See more keywords
Normalized Sign‐Changing Solutions for the Nonlinear Schrödinger Equation With a Mass‐Critical Perturbation
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DOI: 10.1002/mma.10954
Abstract: We investigate the mass‐critical perturbed nonlinear Schrödinger equation with a prescribed mass and establish the existence of sign‐changing normalized solutions in noncompact settings for N≥4$$ N\ge 4 $$ . Additionally, we analyze the asymptotic behavior… read more here.
Keywords: schr dinger; sign changing; normalized solutions; dinger equation ... See more keywords
Optical Solions, Bifurcation Study, and Phase Portraits for the Dual‐Mode Nonlinear SchröDinger Model With Square Root Kerr Law
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DOI: 10.1002/mma.11052
Abstract: In this paper, we studied the bifurcations and dynamical behavior of traveling wave solutions for dual‐mode resonant nonlinear Schrödinger equation using the square root Kerr law. Building upon the traveling wave transformation, the resonant nonlinear… read more here.
Keywords: dual mode; schr dinger; nonlinear schr; square root ... See more keywords
Characteristics of rogue waves on a soliton background in a coupled nonlinear Schrödinger equation
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DOI: 10.1002/mma.5532
Abstract: In this paper, a coupled nonlinear Schrödinger (CNLS) equation, which can describe evolution of localized waves in a two‐mode nonlinear fiber, is under investigation. By using the Darboux‐dressing transformation, the new localized wave solutions of… read more here.
Keywords: coupled nonlinear; waves soliton; nonlinear schr; rogue waves ... See more keywords
Rational and semi‐rational solutions of a nonlocal (2 + 1)‐dimensional nonlinear Schrödinger equation
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DOI: 10.1002/mma.5792
Abstract: We consider the fully parity‐time (PT) symmetric nonlocal (2 + 1)‐dimensional nonlinear Schrödinger (NLS) equation with respect to x and y. By using Hirota's bilinear method, we derive the N‐soliton solutions of the nonlocal NLS… read more here.
Keywords: semi rational; rational solutions; nonlocal dimensional; nonlinear schr ... See more keywords
Exact traveling wave solutions for resonance nonlinear Schrödinger equation with intermodal dispersions and the Kerr law nonlinearity
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DOI: 10.1002/mma.5827
Abstract: The main aim of this article is to present some new exact solutions of the resonant nonlinear Schrödinger equation. These solutions are derived by using the generated exponential rational function method (GERFM). The kink‐type, bright,… read more here.
Keywords: dinger equation; schr dinger; nonlinear schr;
The N‐coupled higher‐order nonlinear Schrödinger equation: Riemann‐Hilbert problem and multi‐soliton solutions
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DOI: 10.1002/mma.6055
Abstract: In this work, the Riemann‐Hilbert (RH) problem of the N‐coupled high‐order nonlinear Schrödinger (N‐CHNLS) equations is studied carefully, which controls the propagation of N fields with all high‐order effects such as high‐order dispersion, self‐steepening effect,… read more here.
Keywords: hilbert problem; order; order nonlinear; problem ... See more keywords
A note on the finite fractal dimension of the global attractors for dissipative nonlinear Schrödinger‐type equations
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DOI: 10.1002/mma.6709
Abstract: In this article, we present, throughout two basic models of damped nonlinear Schrödinger (NLS)–type equations, a new idea to bound from above the fractal dimension of the global attractors for NLS‐type equations. This could answer… read more here.
Keywords: schr dinger; type equations; fractal dimension; nonlinear schr ... See more keywords
Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative
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DOI: 10.1002/mma.7302
Abstract: The paper aims to employ a new effective methodology to build exact fractional solutions to the generalized nonlinear Schrödinger equation with a local fractional operator defined on Cantor sets. The equation contains group velocity dispersion… read more here.
Keywords: generalized nonlinear; nonlinear schr; solutions generalized; equation ... See more keywords