Chirp-free optical dromions for the presence of higher order spatio-temporal dispersions and absence of self-phase modulation in birefringent fibers

2020 ◽  
Vol 34 (35) ◽  
pp. 2050399 ◽  
Author(s):  
Syed Tahir Raza Rizvi ◽  
Aly R. Seadawy ◽  
Ijaz Ali ◽  
Ishrat Bibi ◽  
Muhammad Younis
Keyword(s):  
Differential Equations ◽  
Optical Fiber ◽  
Ordinary Differential Equations ◽  
Elliptic Function ◽  
Phase Modulation ◽  
Model Studies ◽  
Weierstrass Elliptic Function ◽  
Ode Method ◽  
Soliton Transmission ◽  
Spatio Temporal

In this paper, we study Biswas–Arshed (BA) model in birefringent fibers for chirp-free solitons (dromions) with the aid of sub-ordinary differential equations (ODE) method. The BA model studies the soliton transmission in optical fiber. We obtain bright, periodic, and Weierstrass elliptic function solutions with constraint conditions.

scholarly journals Weierstrass elliptic difference equations

1987 ◽  
Vol 35 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Renfrey B. Potts
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Elliptic Function ◽  
Order Differential Equation ◽  
Second Order ◽  
Elliptic Difference ◽  
First Order ◽  
Second Order Differential Equation ◽  
Weierstrass Elliptic Function

The Weierstrass elliptic function satisfies a nonlinear first order and a nonlinear second order differential equation. It is shown that these differential equations can be discretized in such a way that the solutions of the resulting difference equations exactly coincide with the corresponding values of the elliptic function.

scholarly journals On the absence of logarithmic singularities in the solutions of Lamé-type equations

2021 ◽  
Vol 57 (4) ◽  
pp. 428-434
Author(s):  
E. R. Babich ◽  
I. P. Martynov
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Elliptic Function ◽  
Logarithmic Singularity ◽  
Second Order ◽  
Linear Differential Equations ◽  
Regular Singularity ◽  
Weierstrass Elliptic Function ◽  
Logarithmic Singularities ◽  
Linear Differential

The object of this research is linear differential equations of the second order with regular singularities. We extend the concept of a regular singularity to linear partial differential equations. The general solution of a linear differential equation with a regular singularity is a linear combination of two linearly independent solutions, one of which in the general case contains a logarithmic singularity. The well-known Lamé equation, where the Weierstrass elliptic function is one of the coefficients, has only meromorphic solutions. We consider such linear differential equations of the second order with regular singularities, for which as a coefficient instead of the Weierstrass elliptic function we use functions that are the solutions to the first Painlevé or Korteweg – de Vries equations. These equations will be called Lamé-type equations. The question arises under what conditions the general solution of Lamé-type equations contains no logarithms. For this purpose, in the present paper, the solutions of Lamé-type equations are investigated and the conditions are found that make it possible to judge the presence or absence of logarithmic singularities in the solutions of the equations under study. An example of an equation with an irregular singularity having a solution with an logarithmic singularity is given, since the equation, defining it, has a multiple root.

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