Journal ArticleDOI
Soliton-like solutions of a derivative nonlinear Schrödinger equation with variable coefficients in inhomogeneous optical fibers
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TLDR
In this article, a derivative nonlinear Schrodinger equation with variable coefficients is investigated, which governs the propagation of the sub-picosecond soliton pulses in inhomogeneous optical fibers.Abstract:
Under investigation in this paper is a derivative nonlinear Schrodinger equation with variable coefficients, which governs the propagation of the subpicosecond soliton pulses in inhomogeneous optical fibers. Through the nonisospectral Kaup–Newell scheme, the Lax pair is constructed with some constraints on the variable coefficients. Under the integrable conditions, bright one- and multi-soliton-like solutions are derived via the Hirota method. By suitably choosing the dispersion coefficient function, several types of inhomogeneous solitons are obtained in, respectively: (1) exponentially decreasing dispersion profile, (2) linearly decreasing dispersion profile, (3) exponentially increasing dispersion profile, and (4) periodically fluctuating dispersion profile. The intensity of the inhomogeneous soliton can be controlled by means of modifying the loss/gain term. Asymptotic analysis of the two-soliton-like solution is performed, which shows that the changes of the widths, amplitudes, and energies before and after the collision are completely caused by the variable coefficients, but have nothing to do with the collision between two soliton-like envelopes. Through suitable choices of variable coefficients, figures are plotted to illustrate the collision behavior between two inhomogeneous solitons, which has some potential applications in the real optical communication systems.read more
Citations
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Journal ArticleDOI
Quintic time-dependent-coefficient derivative nonlinear Schrödinger equation in hydrodynamics or fiber optics: bilinear forms and dark/anti-dark/gray solitons
TL;DR: In this article, a quintic time-dependent-coefficient derivative nonlinear Schrodinger equation for certain hydrodynamic wave packets or medium with the negative refractive index is investigated.
Journal ArticleDOI
Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects
TL;DR: In this article, a variable-coefficient nonlinear Schrodinger (vc-NLS) equation with fourth-order effects describing an inhomogeneous one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or alpha helical protein was derived.
Journal ArticleDOI
Bäcklund transformations and soliton solutions for a $$(3+1)$$ ( 3 + 1 ) -dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
TL;DR: Based on the binary Bell polynomials, Hirota method, and symbolic computation, the bilinear form is obtained in this paper, and one-and two-soliton solutions are presented.
Journal ArticleDOI
Breather interactions, higher-order rogue waves and nonlinear tunneling for a derivative nonlinear Schrödinger equation in inhomogeneous nonlinear optics and plasmas
TL;DR: In this article, a variable-coefficient derivative nonlinear Schrodinger (vc-DNLS) equation governing the femtosecond pulses in the inhomogeneous optical fibers or nonlinear Alfven waves in a plasmas was investigated.
Journal ArticleDOI
Evolution of optical solitary waves in a generalized nonlinear Schrödinger equation with variable coefficients
TL;DR: In this article, the authors derived exact analytical solutions in terms of rational-like functions for a generalized nonlinear Schrodinger equation with variable coefficients via the methods of similarity transformation and direct ansatz.
References
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Book
Nonlinear Fiber Optics
TL;DR: The field of nonlinear fiber optics has advanced enough that a whole book was devoted to it as discussed by the authors, which has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field.
Book
Darboux transformations and solitons
V. B. Matveev,Mikhail A. Salle +1 more
TL;DR: In this paper, the authors developed a systematic algebraic approach to solve linear and non-linear partial differential equations arising in soliton theory, such as the non-stationary linear Schrodinger equation, Korteweg-de Vries and Kadomtsev-Petviashvili equations, the Davey Stewartson system, Sine-Gordon and nonlinearSchrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.
Book
Optical solitons : from fibers to photonic crystals
TL;DR: In this article, the authors introduce spatial and temporal solitons in photonic crystals, and introduce the concept of Incoherent Solitons, which is a subclass of the spatial and temporally soliton.
Journal ArticleDOI
Exact Solution of the Korteweg-de Vries Equation for Multiple Collisions of Solitons
TL;DR: An exact solution for the Korteweg-de Vries equation for the case of multiple collisions of $N$ solitons with different amplitudes was obtained in this paper, which is the only known exact solution.
Journal ArticleDOI
Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion
Akira Hasegawa,Frederick Tappert +1 more
TL;DR: Theoretical calculations supported by numerical simulations show that utilization of the nonlinear dependence of the index of refraction on intensity makes possible the transmission of picosecond optical pulses without distortion in dielectric fiber waveguides with group velocity dispersion.
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