Results 31 to 40 of about 1,446 (167)

Soliton solutions and a bi-Hamiltonian structure of the fifth-order nonlocal reverse-spacetime Sasa-Satsuma-type hierarchy via the Riemann-Hilbert approach

AIMS Mathematics
Our objective is to explore the intricacies of a nonlinear nonlocal fifth-order scalar Sasa-Satsuma equation in reverse spacetime which is rooted in a nonlocal 5 × 5 matrix AKNS spectral problem.
Ahmed M. G. Ahmed , Alle Adjiri, Solomon Manukure   +2 more
doaj   +1 more source

The Hilbert problem in a half-plane for generalized analytic functions with a singular point on the real axis

Учёные записки Казанского университета: Серия Физико-математические науки
This article analyzes the inhomogeneous Hilbert boundary value problem for an upper half-plane with the finite index and boundary condition on the real axis for one generalized Cauchy–Riemann equation with a singular point on the real axis.
P. L. Shabalin, R. R. Faizov
doaj   +1 more source

Anti-plane crack in human bone. I. Mathematical modelling

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
We consider an anti-plane crack in a bone, considered as an initially deformed orthotropic, linear elastic composite material. Elastic incremental fields in the composite material are obtained following theories of Guz’s representation and of Riemann ...
Crăciun Eduard Marius, Marin Marin, Răbâea Adrian   +2 more
doaj   +1 more source

Well-posedness of discontinuous boundary-value problems for nonlinear elliptic complex equations in multiply connected domains

Electronic Journal of Differential Equations, 2013
In the first part of this article, we study a discontinuous Riemann-Hilbert problem for nonlinear uniformly elliptic complex equations of first order in multiply connected domains. First we show its well-posedness. Then we give the representation of
Guo-Chun Wen
doaj  

Exact solutions of a local fractional nonisospectral complex mKdV equation based on Riemann–Hilbert method with time-varying spectrum

Alexandria Engineering Journal
This article combines the Riemann–Hilbert method with fractional power-law time-varying spectrum for the first time to solve a time fractional nonisospectral complex mKdV (tfniscmKdV) equation. Firstly, the tfniscmKdV equation and its associated Lax pair
Bo Xu, Sheng Zhang
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The Modified Coupled Hirota Equation: Riemann-Hilbert Approach and N-Soliton Solutions

Abstract and Applied Analysis, 2019
The Cauchy initial value problem of the modified coupled Hirota equation is studied in the framework of Riemann-Hilbert approach. The N-soliton solutions are given in a compact form as a ratio of (N+1)×(N+1) determinant and N×N determinant, and the ...
Siqi Xu
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$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework [PDF]

Sahand Communications in Mathematical Analysis, 2019
In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied.
Ali Huseynli, Asmar Mirzabalayeva
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Long-Time Asymptotics of a Three-Component Coupled mKdV System

Mathematics, 2019
We present an application of the nonlinear steepest descent method to a three-component coupled mKdV system associated with a 4 × 4 matrix spectral problem. An integrable coupled mKdV hierarchy with three potentials is first generated. Based
Wen-Xiu Ma
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Riemann-Hilbert approach for the integrable nonlocal nonlinear Schr\"odinger equation with step-like initial data

Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2018
We study the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger (NNLS) equation \[ iq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\bar{q}(-x,t)=0 \] with a step-like initial data: $q(x,0)=o(1)$ as $x\to-\infty$ and $q(x,0)=A+o(1)$ as $x\to\infty ...
Ya. Rybalko, D. G. Shepelsky
doaj  

Crack Propagation in the Human Bone. Mode I of Fracture

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018
The problem of crack propagation in human bone is studied. We for- mulate and solve the mathematical problem for the pre-stressed crack in Mode I of classical fracture.
Craciun E. M., Rabaea A., Popa M. F., Mihailov C. I.   +3 more
doaj   +1 more source