Results 61 to 70 of about 1,989,001 (174)
Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We study the nonlinear Schrödinger equation with a competing cubic–quintic power‐law nonlinearity on the waveguide domain Rx×TLy$\mathbb {R}_x \times \mathbb {T}_{L_y}$. This model is globally well‐posed and admits line solitary wave solutions, whose transverse (in‐)stability is numerically investigated.
Christian Klein, Christof Sparber
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Multiple front and pulse solutions in spatially periodic systems
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
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Dispersion‐Less Dissipative Soliton Fiber Laser
Laser &Photonics Reviews, Volume 20, Issue 6, 18 March 2026.A dispersion‐less fiber laser architecture generates high‐energy, pedestal‐free picosecond pulses without resorting to conventional pulse stretching. This energy‐managed laser achieves remarkable flexibility in pulse parameters, delivering up to 0.54 μJ$\mathrm{\mu}\mathrm{J}$ pulses with minimal spectral distortion using standard telecom components ...
Mostafa I. Mohamed +2 more
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Completely integrable nonlinear Schrödinger type equations on moving space curves
, 1997 Using the Lamb formalism, we show that some completely integrable homogeneous and inhomogeneous nonlinear Schrödinger (NLS) type equations such as derivative NLS, extended NLS, higher-order NLS, inhomogeneous NLS, circularly and radially symmetric NLS ...
Porsezian, K.
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Dispersive Wave Focusing in Shoaling Water With Currents
Journal of Geophysical Research: Oceans, Volume 131, Issue 3, March 2026.Abstract A methodology creating dispersive focusing waves on constant depth, originally proposed by Rapp and Melville (1990), https://doi.org/10.1098/rsta.1990.0098, has provided a wide range of applications studying nonlinear waves, wave breaking, and rogue waves in the open ocean.
Y. Watanabe, T. Davey, D. M. Ingram
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Numerical Study of a Nonlocal Nonlinear Schrödinger Equation (MMT Model)
Studies in Applied Mathematics, Volume 156, Issue 3, March 2026.ABSTRACT In this paper, we study a nonlocal nonlinear Schrödinger equation (MMT model). We investigate the effect of the nonlocal operator appearing in the nonlinearity on the long‐term behavior of solutions, and we identify the conditions under which the solutions of the Cauchy problem associated with this equation are bounded globally in time in the ...
Amin Esfahani, Gulcin M. Muslu
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Surface Wave Solutions in 1D and 2D for the Broer–Kaup–Boussinesq–Kupershmidt System
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT The Broer–Kaup–Boussinesq–Kupershmidt (BKBK) system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification introduces backward diffusion terms proportional to a real parameter κ$\kappa$.
Darryl D. Holm, Ruiao Hu, Hanchun Wang
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Bright and Dark Breathers on an Elliptic Wave in the Defocusing mKdV Equation
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT Breathers on an elliptic wave background consist of nonlinear superpositions of a soliton and a periodic wave, both traveling with different wave speeds and interacting periodically in the space‐time. For the defocusing modified Korteweg–de Vries equation, the construction of general breathers has been an open problem since the elliptic wave ...
Dmitry E. Pelinovsky, Rudi Weikard
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International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.We study the initial value problem for the Majda–McLaughlin–Tabak model i∂tu+−∂x2α/2u=κDxβDxβu2Dxβu,ux,0=u0x, x∈R,t∈R, for α = 2 and −(1/4) < β < 1/2 with β ≠ 0, where u≔u(x, t) is a complex‐valued function. We show that the uniform radius of spatial analyticity σ(t) of the solutions at time t is bounded from below by c|t|−1/(2γ) for some positive ...
Tegegne Getachew +2 more
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Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.In this paper, we consider the initial value problem associated with the cubic nonlinear Schrödinger equation with third‐order dispersion ∂tu+iα∂x2u+β∂x3u+iγu2u=0,x∈ℝ,t∈ℝ,ux,0=u0x, where α, β and γ are real constants such that β, γ ≠ 0, u is a complex valued function and the initial data u0 is analytic on ℝ and has a uniform radius of analyticity σ0 in
Tegegne Getachew, Xiasheng Shi
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