Nanoptera in higher-order nonlinear Schrödinger equations: effects of discretization
DOI10.1007/s00332-022-09834-5OpenAlexW4309891630MaRDI QIDQ2105224
Aaron J. Moston-Duggan, Mason A. Porter, Christopher J. Lustri
Publication date: 8 December 2022
Published in: Journal of Nonlinear Science (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.08407
discretizationnonlinear wavesnanopteraexponential asymptotic analysishigher-order NLS equationsKarpman equations
Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Bifurcations in context of PDEs (35B32) Traveling wave solutions (35C07) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41) PDEs on time scales (35R07)
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Cites Work
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- Structural stability of the Korteweg-de Vries solitons under a singular perturbation
- Stokes' phenomenon; smoothing a Victorian discontinuity
- The discrete nonlinear Schrödinger equation. Mathematical analysis, numerical computations and physical perspectives
- Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- The devil's invention: Asymptotic, superasymptotic and hyperasymptotic series
- Solitons on lattices
- A new barrier to the existence of moving kinks in Frenkel-Kontorova lattices
- Nanopteron solutions of diatomic Fermi-Pasta-Ulam-Tsingou lattices with small mass-ratio
- Spatial properties and numerical solitary waves of a nonintegrable discrete nonlinear Schrödinger equation with nonlinear hopping
- Numerical results on existence and stability of standing and traveling waves for the fourth order beam equation
- Solitons of the fourth order nonlinear Schrödinger equation
- Evolution of solitons described by higher-order nonlinear Schrödinger equations
- Lyapunov approach to the soliton stability in highly dispersive systems. I: Fourth order nonlinear Schrödinger equations
- Nanoptera in nonlinear woodpile chains with zero precompression
- Existence and stability of discrete solitons in nonlinear Schrödinger lattices with hard potentials
- On the normalized ground states for the Kawahara equation and a fourth order NLS
- Nanoptera and Stokes curves in the 2-periodic Fermi-Pasta-Ulam-Tsingou equation
- One-parameter localized traveling waves in nonlinear Schrödinger lattices
- Travelling solitary waves in the discrete Schrödinger equation with saturable nonlinearity: Existence, stability and dynamics
- Stability of discrete solitons in nonlinear Schrödinger lattices
- Asymptotics beyond all orders and Stokes lines in nonlinear differential-difference equations
- Solitary waves and stable analysis for the quintic discrete nonlinear Schrödinger equation
- Continuum approach to discreteness
- Exponential Asymptotics and Stokes Line Smoothing for Generalized Solitary Waves
- On the higher–order Stokes phenomenon
- Nonlinear Waves in Integrable and Nonintegrable Systems
- On the non-universality of the error function in the smoothing of stokes discontinuities
- Nanoptera in a Period-2 Toda Chain
- Variational approximations for traveling solitons in a discrete nonlinear Schrödinger equation
- Exponential asymptotics of a fifth-order partial differential equation
- Exact stationary solutions for the translationally invariant discrete nonlinear Schrödinger equations
- The Defocusing Nonlinear Schrödinger Equation
- Discrete Traveling Solitons in the Salerno Model
- Split-Step Methods for the Solution of the Nonlinear Schrödinger Equation
- A numerical calculation of a weakly non-local solitary wave: the ϕ4breather
- Exponential asymptotics and Stokes lines in nonlinear ordinary differential equations
- A note on the interaction between solitary waves in a singularly-perturbed Korteweg-de Vries equation
- Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg–De Vries Equation
- Stokes phenomena in discrete Painlevé II
- Uniform asymptotic smoothing of Stokes’s discontinuities
- Stokes Phenomenon and Matched Asymptotic Expansions
- Nonintegrable spatial discrete nonlocal nonlinear schrödinger equation
- Nanoptera in Weakly Nonlinear Woodpile Chains and Diatomic Granular Chains
- Mixed dispersion nonlinear Schrödinger equation in higher dimensions: theoretical analysis and numerical computations
- Nanopteron-stegoton traveling waves in spring dimer Fermi-Pasta-Ulam-Tsingou lattices
- Generalized solitary waves in a finite‐difference Korteweg‐de Vries equation
- Standing lattice solitons in the discrete NLS equation with saturation
- Traveling waves and their tails in locally resonant granular systems
- Stokes phenomena in discrete Painlevé I
- Stability of discrete dark solitons in nonlinear Schrödinger lattices
- Exponential asymptotics and Stokes lines in a partial differential equation
- Stability of localized structures in generalized DNLS equations near the anti-continuum limit
- On the formation of bound states by interacting nonlocal solitary waves
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