dinger Equations
Discrete Schrödinger equations in the nonperiodic and superlinear cases: homoclinic solutions
... Using variational methods, we study the existence and multiplicity of homoclinic solutions for a class of discrete Schrödinger equations in infinite m-dimensional lattices with nonlinearities being superlinear at ...
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Ground state solutions for periodic discrete nonlinear Schrödinger equations with saturable nonlinearities
... In this paper, we study a class of periodic discrete nonlinear Schrödinger equations with asymptotically linear nonlinearities, and prove the existence of ground state solutions (i.e., nontrivial solutions with ...
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Multiple solutions of discrete Schrödinger equations with growing potentials
... The discrete nonlinear Schrödinger equation is one of the most important discrete mod- els, which plays an important role in many fields; for example, in biomolecular chains [], nonlinear optics [], Bose-Einstein ...
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New spectral collocation algorithms for one and two dimensional Schrödinger equations with a Kerr law nonlinearity
... Recently, the analytical and numerical solutions of different types of the previous clas- sical Schrödinger equations were discussed in [, ], and for recent schemes for solving PDEs see [–]. Here, we focus ...
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Multiple soliton solutions and a generalized double Wronskian determinant to the \((2+1)\) dimensional nonlinear Schrödinger equations
... In summary, by using the Hirota method and the Wronskian technique, the multiple- soliton solutions and the double Wronskian form satisfying a matrix equation to system () have been presented, respectively. As is well ...
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A new high order compact ADI finite difference scheme for solving 3D nonlinear Schrödinger equation
... The alternating direction implicit (ADI) method is widely used to solve the multi- dimensional Schrödinger equations due to its unconditional stability and efficiency in sav- ing CPU time, see for instance Xu and ...
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Exponential time differencing schemes for the 3 coupled nonlinear fractional Schrödinger equation
... During the last few years, the nonlinear fractional Schrödinger equation (NFSE) has been widely used in modeling physical phenomena such as the propagation of waves in op- tics and hydrodynamics, see [1–4] for details. ...
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Exact and approximate solutions for the fractional Schrödinger equation with variable coefficients
... famous nonlinear Schrödinger equations in an optical fiber [25–27]. Here u(z, t) is the complex envelope of the electrical field, z is the normalized propagation distance along the fiber, t is the retarded time and ...
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Non polynomial spline method for the time fractional nonlinear Schrödinger equation
... research about studying quantum phenomena by fractional calculus. The time-fractional Schrödinger equation is a fundamental equation of fractional quantum mechanics which can be obtained from the classical Schrödinger ...
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Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere
... The results on the Schrödinger map equation are much more fruitful than those on the LLG equation. There are a lot fruitful results on the existence, uniqueness, and the blowup property and soliton solution of the ...
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Conservative Fourier spectral scheme for the coupled Schrödinger–Boussinesq equations
... It is well known that the conservative schemes perform better than the nonconserva- tive ones. Thus, it is of interest to investigate conservative schemes for the CSB system. The Fourier pseudospectral method has ...
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Random attractors for the stochastic damped Klein Gordon Schrödinger system
... In recent decades, much attention has been paid to the existence of random attractor for stochastic partial differential equations. To the authors’ knowledge, Crauel and Flandoli [] and Flandoli and Schmalfuß [] ...
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Some Basic Difference Equations of Schrödinger Boundary Value Problems
... fference equations which are related to discretizations of Schr ¨odinger equations on time scales with special symmetry properties, namely, so-called basic discrete ...¨odinger equations on these ...
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The global solution of anisotropic fourth order Schrödinger equation
... where a < 0, α > 0, b are real numbers. u(x, t) is unknown complex function, ϕ(x) is the given initial value data. The above equations can be used to describe some physical phe- nomena. For example, [1] used ...
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Modulational instability and higher order rogue wave solutions for an integrable generalization of the nonlinear Schrödinger equation in monomode optical fibers
... Recently, rogue waves (RWs) have attracted more and more theoretical and experimental attention []. The RWs were first observed in deep oceans, and later these studies gradu- ally extended to other fields, such as fiber ...
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Exact spatiotemporal soliton solutions to the generalized three dimensional nonlinear Schrödinger equation in optical fiber communication
... As is known to all, there are many kinds of powerful methods to obtain the exact solu- tions of various nonlinear wave equations such as the NLS-type equations. For example, inverse scattering method [], ...
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The intervals of oscillations in the solutions of the radial Schrödinger differential equation
... ] equations (Section .). Our analysis of these equations makes use of a program that was described in [] by CGK for investigating the x-intervals in which the solutions exhibit an oscillatory ...
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Riemann–Hilbert approach and N soliton solution for an eighth order nonlinear Schrödinger equation in an optical fiber
... In recent years, researchers have devoted their attention to many higher-order NLS equations truncating from Equation (1). For instance, an eighth-order NLS equation was under study [9]. The interactions among ...
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The general mixed nonlinear Schrödinger equation: Darboux transformation, rogue wave solutions, and modulation instability
... Equations () and () give us the new solutions after a Darboux transformation, and we can use the results of () and () to get two-order and three-order rogue wave solutions. In the next section, we will ...
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RETRACTED ARTICLE: Sign changing solutions to Schrödinger Kirchhoff type equations with critical exponent
... modulus). Equations of this type arise in the study of string or membrane vibration and were proposed by Kirchhoff in (see []) to describe the transversal os- cillations of a stretched string, particularly, ...
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