Results 41 to 50 of about 62,135,588 (169)
Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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Review of Some Modified Generalized Korteweg–De Vries–Kuramoto–Sivashinsky (mgKdV-KS) Equations
FoundationsThis paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg–De Vries equation, the Kuramoto–Sivashinsky equation, the generalized Korteweg–De Vries–Kuramoto–Sivashinsky equation and the nonhomogeneous ...
Marie-Thérèse Aimar +1 more
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Advances in Mathematical Physics, 2019 The Sawada-Kotera equation with a nonvanishing boundary condition, which models the evolution of steeper waves of shorter wavelength than those depicted by the Korteweg de Vries equation, is analyzed and also the perturbed Korteweg de Vries (pKdV ...
Abdullahi Rashid Adem +3 more
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Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain
Boundary Value Problems, 2017 In this paper, we address an inverse problem for the Korteweg-de Vries equation posed on a bounded domain with boundary conditions proposed by Colin and Ghidaglia.
Mo Chen
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Sharp Upper Bound for Amplitudes of Finite‐Gap Solutions of the Modified Korteweg‐de Vries Equation
Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT A sharp upper bound is established for the amplitudes of finite‐gap solutions of the focusing modified Korteweg–de Vries equation. The proof shows that the optimization can be carried out entirely within the finite‐dimensional hierarchy, without explicit integration of the finite‐gap solution. The maximal amplitude is expressed in terms of the
Otis C. Wright III
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Studies in Applied Mathematics, Volume 157, Issue 3, September 2026.ABSTRACT We construct Lax pairs for the recently (2023) introduced integrable PDE systems known as the BKM equations. As many known and previously studied integrable systems are special cases of the BKM systems, our construction provides Lax pairs for many integrable hierarchies, including previously studied ones such as Camassa–Holm, Dullin–Gottwald ...
Andrey Yu. Konyaev, Vladimir S. Matveev
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Towards quantum hierarchy for the Gromov–Witten theory of elliptic curves
Bulletin of the London Mathematical Society, Volume 58, Issue 9, September 2026.Abstract We construct the quantum double ramification (DR) hierarchy associated with the Gromov–Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the DR cycle, the Gromov–Witten classes of the elliptic curve, and the Hodge class λg−1$\lambda _{g-1}$, together with vanishing results for λg−2$\lambda ...
Paolo Rossi +2 more
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A new approach for the analysis of evolution partial differential equations on a finite interval
Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.Abstract We show that, for certain evolution partial differential equations, the solution on a finite interval (0,ℓ)$(0,\ell)$ can be reconstructed as a superposition of restrictions to (0,ℓ)$(0,\ell)$ of solutions to two associated partial differential equations posed on the half‐lines (0,∞)$(0,\infty)$ and (−∞,ℓ)$(-\infty,\ell)$.
Türker Özsarı +2 more
wiley +1 more source
Observations of High‐Frequency Internal Waves Near Submesoscale Fronts
Journal of Geophysical Research: Oceans, Volume 131, Issue 8, August 2026.Abstract Nonlinear high‐frequency internal waves (HIWs) can occur at oceanic frontal interfaces but are rarely observed directly. This study presents field observations of HIWs near submesoscale fronts (SFs) in the northern Gulf of Mexico. A marine X‐band radar detected a series of organized bands, with a spacing of 50 ∼ 300 m, near SFs.
Mingming Shao +8 more
wiley +1 more source
The Extended Korteweg-de Vries Equation [PDF]
, 1982 A slight and natural extension of the traditional Korteweg-de Vries equation (KdV) allows all (or groups) of its solitons to have the same velocity thus facilitating the application of the KdV to realistic quantum mechanical ...
Hefter, E.F.
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