Results 41 to 50 of about 6,585,637 (137)
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper presents an analysis of breather soliton solutions of the integrable extended KdV and KP equations in (2 + 1)‐ and (3 + 1)‐dimensional settings. Employing symbolic computation along with Hirota’s bilinear formalism, we construct positive logarithmic function solutions for the corresponding bilinear equations associated with each model. These
Ali Danladi +4 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.A new negative‐order form of the (3 + 1)‐dimensional Calogero–Bogoyavlenskii–Schiff equation is examined in this investigation. This equation plays an important role in accurately describing the thermodynamic properties of mixtures, particularly in chemical engineering applications.
Ulviye Demirbilek +6 more
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Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT As part of the efforts aimed at extending Painlevé and Gambier's work on second‐order equations in one variable to first‐order ones in two, in 1981, Bureau classified the systems of ordinary quadratic differential equations in two variables which are free of movable critical points (which have the Painlevé Property).
Adolfo Guillot
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MathematicsThe second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean.
Nikolay A. Kudryashov, Sofia F. Lavrova
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A topological algorithm for the Fourier transform of Stokes data at infinity
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract We give a topological description of the behaviour of Stokes matrices under the Fourier transform from infinity to infinity in a large number of cases of one level. This explicit, algorithmic statement is obtained by building on a recent result of T.
Jean Douçot, Andreas Hohl
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An Extended Complex Method to Solve the Predator–Prey Model
AxiomsThrough transformation and utilizing a novel extended complex method combining with the Weierstrass factorization theorem, Wiman–Valiron theory and the Painlevé test, new non-constant meromorphic solutions were constructed for the predator–prey model ...
Hongqiang Tu, Guoqiang Dang
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Engineering Reports, Volume 7, Issue 6, June 2025.This study explores novel nonlinear dynamical solutions to the (2 + 1)‐dimensional variable coefficient equation in oceanography. Using the Hirota bilinear method, we derive multi‐soliton, M‐lump, and hybrid wave solutions, revealing collision phenomena and their physical significance in nonlinear fluid dynamics and mathematical physics.
Hajar F. Ismael +3 more
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Studies in Applied Mathematics, Volume 154, Issue 4, April 2025.ABSTRACT In this paper, we compute the small and large x$x$ asymptotics of the special function solutions of the Painlevé‐III equation in the complex plane. We use the representation in terms of Toeplitz determinants of Bessel functions obtained by Masuda. Toeplitz determinants are rewritten as multiple contour integrals using Andrèief's identity.
Hao Pan, Andrei Prokhorov
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 4, Page 5039-5063, 15 March 2025.This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation.
Oke Davies Adeyemo
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