Results 51 to 60 of about 1,989,001 (174)
Self‐Similar Blowup for the Cubic Schrödinger Equation
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1831-1918, August 2026.ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
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Integrable discretisations and Yang–Baxter maps for super nonlinear Schrödinger systems
Nuclear Physics BWe construct an integrable Grassmann-extended vertex-bond discrete system, which can be restricted to the Grassmann-extended Adler–Yamilov system of partial difference equations, and we derive a Darboux matrix and a Bäcklund transformation for the latter.
Sotiris Konstantinou-Rizos
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Solution of the Davey–Stewardson equation using homotopuy analysis method
Nonlinear Analysis, 2010 In this paper, the homotopy analysis method (HAM) proposed by Liao is adopted for solving Davey–Stewartson (DS) equations which arise as higher dimensional generalizations of the nonlinear Schrödinger (NLS) equation. The results obtained by HAM have been
H. Jafari, M. Alipour
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A Hybrid ML‐PDE Framework for Predicting Breaking Ocean Waves
Journal of Geophysical Research: Machine Learning and Computation, Volume 3, Issue 4, August 2026.Abstract Wave breaking plays a central role in ocean dynamics, dissipating wave energy and shaping the evolution of the sea surface. Yet, breaking remains difficult to model: envelope‐based models efficiently capture nonlinear wave evolution and are interpretable but exclude breaking, while high‐fidelity direct numerical simulations resolve breaking ...
Y. Liu +3 more
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Schrödinger equations in nonlinear systems
, 2019 This book explores the diverse types of Schrödinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose–Einstein Condensates.
Kengne, Emmanuel, Liu, Wu-Ming
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Engineering Reports, Volume 8, Issue 7, July 2026.Analytical fuzzy soliton solutions of a modified space–time fractional ϕ4$$ {\phi}^4 $$ model are derived using EHFM, capturing memory effects and uncertainty. Results reveal diverse wave structures and show how fractional order and fuzziness significantly influence soliton amplitude, localization, and propagation, with heightened sensitivity near the ...
Mohsin Khalid +3 more
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Finite difference scheme for two-dimensional periodic nonlinear Schrödinger equations
, 2021 A nonlinear Schrödinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schrödinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations.
Nakamura, Shohei +3 more
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An Explicit Construction of Kaleidocycles by Elliptic Theta Functions
Studies in Applied Mathematics, Volume 156, Issue 5, May 2026.ABSTRACT We study a configuration space consisting of ordered points on the two‐dimensional sphere satisfying a system of quadratic constraints. We construct explicit periodic orbits in the configuration space using elliptic theta functions. The constructed orbits simultaneously satisfy semi‐discrete analogues of the modified KdV and sine‐Gordon ...
Shizuo Kaji +2 more
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We investigate the existence and spectral stability of traveling wave solutions for a class of fourth‐order semilinear wave equations, commonly referred to as beam equations. Using variational methods based on a constrained maximization problem, we establish the existence of smooth, exponentially decaying traveling wave profiles for wavespeeds
Vishnu Iyer +2 more
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Optimal solution of nonlinear equations [PDF]
, 1985 journal articleWe survey recent worst case complexity results for the solution of nonlinear equations. Notes on worst and average case analysis of iterative algorithms and a bibliography of the subject are also ...
Optimal solution; Nonlinear equations +1 more
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