Results 41 to 50 of about 249 (94)

Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modeling [PDF]

We undertake a detailed comparison of the results of direct numerical simulations of the integrable soliton gas dynamics with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons.
Carbone, Francesco, Dutykh, Denys, El, Gennady   +2 more
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Fractional Analogous Models in Mechanics and Gravity Theories

We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange--Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity and fractional
D Baleanu, D Baleanu, S Anco, S Vacaru, S Vacaru, S Vacaru   +5 more
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On Darboux transformations for the derivative nonlinear Schr\"odinger equation [PDF]

We consider Darboux transformations for the derivative nonlinear Schr\"odinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented and proved.
Nimmo, Jonathan J. C., Yilmaz, Halis
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Chaotic and quasi-periodic dynamics in nonlinear micro-strain wave systems: Exact symbolic solutions and symmetry-based analysis

Results in Engineering
This work presents a systematic theoretical and computational investigation of the micro-strain wave (MSW) model, a fundamental nonlinear evolution equation governing propagation phenomena in media with microscale deformation effects.
Mostafa M.A. Khater
doaj   +1 more source

Rogue waves of the Fokas-Lenells equation

The Fokas-Lenells (FL) equation arises as a model eqution which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order (in the leading asymptotic order the nonlinear Schr\"odinger (NLS ...
He, Jingsong, Porsezian, Kuppuswamy, Xu, Shuwei   +2 more
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Mathematical analysis of some new adequate broad-ranging soliton solutions of nonlinear models through the recent technique

Partial Differential Equations in Applied Mathematics
The Bogoyavlenskii and the simplified modified Camassa-Holm (SMCH) models are studied through the recent technique namely auxiliary equation method in this paper.
M. Ashikur Rahman, M. Al-Amin, Mst. Kamrunnaher, M. Abul Kawser, Rajaul Haque, M. Ali Akbar, M. Nurul Islam   +6 more
doaj   +1 more source

Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics

Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics.
Dumitru Baleanu, Gorenflo R., Kilbas A. A., Sergiu I. Vacaru   +3 more
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The continuous classical Heisenberg ferromagnet equation with in-plane asymptotic conditions. I. Direct and inverse scattering theory [PDF]

We develop the direct and inverse scattering theory of the linear eigenvalue problem associated with the classical Heisenberg continuous equation with in-plane asymptotic conditions.
Demontis, Francesco, Ortenzi, Giovanni, Sommacal, Matteo, van der Mee, Cornelis   +3 more
core   +1 more source

Solitons of a simple nonlinear model on the cubic lattice

We study a simple nonlinear model defined on the cubic lattice. We propose a bilinearization scheme for the field equations and demonstrate that the resulting system is closely related to the well-studied integrable models, such as the Hirota bilinear ...
Vekslerchik, V. E.
core   +2 more sources

Time-dependent Schroedinger equation in dimension $k+1$: explicit and rational solutions via GBDT and multinodes

A version of the binary Darboux transformation is constructed for non-stationary Schroedinger equation in dimension $k+1$, where $k$ is the number of space variables, $k \geq 1$. This is an iterated GBDT version. New families of non-singular and rational
Sakhnovich, A. L.
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