Results 11 to 20 of about 10,797 (309)

A Hyperbolic Approximation of the Nonlinear Schrödinger Equation

Studies in Applied Mathematics
ABSTRACT We study a first‐order hyperbolic approximation of the nonlinear Schrödinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian structure, along with at least three conserved quantities that approximate those of NLS.
Abhijit Biswas, Laila S. Busaleh, David I. Ketcheson, Carlos Muñoz‐Moncayo, Manvendra Rajvanshi   +4 more
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Dynamical investigation of the nonlinear Schrödinger equation with second-order spatiotemporal involvement of the time-conformable operator

Nonlinear Analysis
The article analyzes the application of the extended hyperbolic function technique to a conformable-operator nonlinear Schrödinger equation, incorporating group velocity dispersion coefficients and second-order spatiotemporal components.
Muhammad Amin S. Murad, Faraidun Kadir Hamasalh, Mujahid Iqbal, Sandeep Malik, Ahmed H. Arnous   +4 more
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Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation [PDF]

Journal of Applied Mathematics, 2013
We consider the Cauchy problem for the damped nonlinear hyperbolic equation inn-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.
Yu-Zhu Wang
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]

, 2015
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian, Moro, A., Antonio Moro, Klein, C, Moro, Anotnio, Grava, T., Dubrovin, Boris, Boris Dubrovin, Dubrovin, B., Moro, Antonio, Tamara Grava, Klein, C., Grava, Tamara, Christian Klein   +13 more
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Approximate analytical solutions of nonlinear hyperbolic partial differential equation [PDF]

, 2022
The Multistep Modified Reduced Differential Transform Method (MMRDTM) is proposed and implemented in this study to obtain solutions of hyperbolic partial differential equations. We examine at the nonlinear Schrodinger equation (NLSE).
Suriana Lasairaya, Che Haziqah Che Hussin, Arif Mandangan, Darmesah Gabda   +3 more
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Weak Solutions for a Simple Hyperbolic System [PDF]

, 2001
The model studied concerns a simple first-order hyperbolic system. The solutions in which one is most interested have discontinuities which persist for all time, and therefore need to be interpreted as weak solutions.
Lyne, Owen D., Williams, David S.
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Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations

Journal of Applied Mathematics, 2012
With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way.
Zeid I. A. Al-Muhiameed, Emad A.-B. Abdel-Salam   +1 more
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Exact and Fast Numerical Algorithms for the Stochastic Wave Equation [PDF]

, 2003
On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions.
Martin, A., Prigarin, Sergej M., Winkler, Gerhard, Sergei M. Prigarin, Winkler, G., Martin, Andreas, Prigarin, S.M., Prigarin, Sergej, Andreas Martin, Gerhard Winkler   +9 more
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On nonlinear evolution equation of second order in Banach spaces

Open Mathematics, 2018
Here we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the ...
Soltanov Kamal N.
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Oscillation of Nonlinear Hyperbolic Differential Equations with Impulses [PDF]

Nonlinear Oscillations, 2004
We study oscillatory properties of solutions of nonlinear impulsive hyperbolic differential equations and find new necessary and sufficient conditions for the existence of oscillations.
Anping Liu, Xiao, L., Mengxing He
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