Nonlinear Optical Waves

Maĭmistov, A. I.; Башаров, А. М.

doi:10.1007/978-94-017-2448-7

Cited by 246 publications

(138 citation statements)

References 0 publications

Supporting

Mentioning

127

Contrasting

Unclassified

Order By: Relevance

“…The error thus goes from v −(1−ǫ)/2 at t = t 2 to v −(1−ǫ)/2+ǫ at t = t 3 . That is done by a well known computation [14], [13,Sect.3.4] which reappears in many scattering theories, from the free S-matrix in automorphic scattering, to Eckart barriers in quantum chemistry. We quote the results:…”

Section: Review Of Theoretical Methodsmentioning

confidence: 99%

Soliton Splitting by External Delta Potentials

2007

View full text Add to dashboard Cite

Abstract. We show that a soliton scattered by an external delta potential splits into two solitons and a radiation term. Theoretical analysis gives the amplitudes and phases of the reflected and transmitted solitons with errors going to zero as the velocity of the incoming soliton tends to infinity. Numerical analysis shows that this asymptotic relation is valid for all but very slow solitons.We also show that the total transmitted mass, that is the square of the L 2 norm of the solution restricted on the transmitted side of the delta potential is in good agreement with the quantum transmission rate of the delta potential.

show abstract

Section: Review Of Theoretical Methodsmentioning

confidence: 99%

Soliton Splitting by External Delta Potentials

2007

View full text Add to dashboard Cite

show abstract

“…For u 0 (x) = αsechx, 0 ≤ α ≤ 1, we have η = (2α − 1) + -see [12,Sect.3.4]. In the case α = 1/2 we have a zero resonance (a real spectral singularity).…”

Section: Phasementioning

confidence: 99%

Fast Soliton Scattering by Delta Impurities

Holmer

Marzuola

Zworski

2007

Commun. Math. Phys.

140

214

View full text Add to dashboard Cite

Abstract. We study the Gross-Pitaevskii equation with a repulsive delta function potential. We show that a high velocity incoming soliton is split into a transmitted component and a reflected component. The transmitted mass (L 2 norm squared) is shown to be in good agreement with the quantum transmission rate of the delta function potential. We further show that the transmitted and reflected components resolve into solitons plus dispersive radiation, and quantify the mass and phase of these solitons.

show abstract

“…(25) equal zero and the initial shape of the pulses is the function of secant hyperbolic form, the equation will have the soliton solutions [27,30]. These solitons exhibit the periodic feature with a characteristic period during propagation.…”

Section: Iii2 the Fourth Order Runge-kutta Algorithmmentioning

confidence: 99%

“…These results are in good agreement with analytical predictions about the periodic feature in the evolution of the envelope function. Analytical expressions for the higher-order solitons are very complicated and only in the case of the second-and third-order they are explicitly given in literature [11,27,30], but for the tenth-order soliton considered above it is presented only by numerical results.…”

Section: Iii2 the Fourth Order Runge-kutta Algorithmmentioning

confidence: 99%

Propagation of Ultrashort Pulses in a Nonlinear Medium

Van¹,

Thuan²,

Goldstein³

et al. 2010

CMST

View full text Add to dashboard Cite

Abstract:In this paper, using a general propagation equation of ultrashort pulses in an arbitrary dispersive nonlinear medium derived in [8] we study in the specific case of Kerr media. An obtained ultrashort pulse propagation equation which is called Generalized Nonlinear Schrödinger Equation usually has a very complicated form and looking for its solutions is usually a "mission impossible". Theoretical methods to solve this equation are effective only for some special cases. As an example we describe the method of a developed elliptic Jacobi function expansion. Several numerical methods of finding approximate solutions are simultaneously used. We focus mainly on the following methods: Split-Step, Runge-Kutta and Imaginary-time algorithms. Some numerical experiments are implemented for soliton propagation and interacting high order solitons. We consider also an interesting phenomenon: the collapse of solitons.

show abstract

Nonlinear Optical Waves

Cited by 246 publications

References 0 publications

Soliton Splitting by External Delta Potentials

Soliton Splitting by External Delta Potentials

Fast Soliton Scattering by Delta Impurities

Propagation of Ultrashort Pulses in a Nonlinear Medium

Contact Info

Product

Resources

About