Results 21 to 30 of about 70 (63)

Compatible flat metrics

Journal of Applied Mathematics, Volume 2, Issue 7, Page 337-370, 2002., 2002
We solve the problem of description of nonsingular pairs of compatible flat metrics for the general N‐component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated.
Oleg I. Mokhov
wiley   +1 more source

Chains of KP, semi‐infinite 1‐Toda lattice hierarchy and Kontsevich integral

Journal of Applied Mathematics, Volume 1, Issue 4, Page 175-193, 2001., 2001
There are well‐known constructions of integrable systems that are chains of infinitely many copies of the equations of the KP hierarchy “glued” together with some additional variables, for example, the modified KP hierarchy. Another interpretation of the latter, in terms of infinite matrices, is called the 1‐Toda lattice hierarchy.
L. A. Dickey
wiley   +1 more source

About seismic tomography algorithm in the prediction of geological dislocations in coal seams

Горные науки и технологии, 2018
An algorithm for processing of crosshole seismic survey data enabling recognizing the type and evaluate the characteristics of geological anomalies using a system of criteria is described.
A. V. Antsiferov, A. A. Glukhov, V. V. Tumanov, D. V. Son, S. P. Olenjuk   +4 more
doaj   +1 more source

High order multiscale analysis of discrete integrable equations [PDF]

Open Communications in Nonlinear Mathematical Physics
In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions
Rafael Hernandez Heredero, Decio Levi, Christian Scimiterna   +2 more
doaj   +1 more source

Low regularity conservation laws for Fokas-Lenells equation and Camassa-Holm equation

Advances in Nonlinear Analysis
In this article, we mainly prove low regularity conservation laws for the Fokas-Lenells equation in Besov spaces with small initial data both on the line and on the circle. We develop a new technique in Fourier analysis and complex analysis to obtain the
Shan Minjie, Chen Mingjuan, Lu Yufeng, Wang Jing   +3 more
doaj   +1 more source

A Symmetry‐Compatible Auxiliary‐Field Splitting of the Korteweg–de Vries Equation: Exact Linearisation via the Direct and Inverse Pathways

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This paper introduces a symmetry‐compatible exact linearisation of the Korteweg–de Vries (KdV) equation through an auxiliary‐field splitting based on Q = νfx. The term ‘symmetry’ is used here in a structural sense; the linear operator is held fixed across solution families, rather than in the sense of Lie point symmetry groups.
Jorge Rodolfo Silva Zabadal, Claudio Zen Petersen, Vinicius Gadis Ribeiro, Ederson Staudt, Huaiqin Wu   +4 more
wiley   +1 more source

The Nonlinear Schrödinger Equation Derived From the Fifth‐Order Korteweg–de Vries Equation Using Multiple Scales Method

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
The mathematical models of problems that arise in many branches of science are nonlinear equations of evolution (NLEE). For this reason, NLEE have served as a language in formulating many engineering and scientific problems. Although the origin of nonlinear evolution equations dates back to ancient times, significant developments have been made in ...
Murat Koparan, Salim A. Messaoudi
wiley   +1 more source

Bäcklund–Darboux Transformations and Discretizations of Super KdV Equation

, 2014
. For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations.
Xue, L.L., Qing Ping Liu, Liu, Q.P., Ling-ling Xue   +3 more
core   +1 more source

Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
doaj   +1 more source

Rogue peakon, posedness and blow-up phenomenon for an integrable Camassa–Holm type equation

Advances in Nonlinear Analysis
In this paper, we study an integrable Camassa–Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon ...
Zhu Mingxuan, Qiao Zhijun, Wang Zhidong, Jiang Zaihong   +3 more
doaj   +1 more source