Lakshmanan Porsezian Daniel Equation Research Articles

Exact multisolitons of noncommutative and commutative Lakshmanan–Porsezian–Daniel equation

We propose and study a noncommutative generalization of Lakshmanan–Porsezian–Daniel equation. For this generalization, we demonstrate its integrability by constructing its zero curvature representation, Darboux transformation and multisoliton solutions. The soliton solutions up to fifth order are presented explicitly within framework of quasideterminants.

Rogue wave solutions of the vector Lakshmanan–Porsezian–Daniel equation

We use a nonrecursive Darboux transformation method to obtain a special hierarchy of rogue wave solutions of the vector Lakshmanan–Porsezian–Daniel equation, which can govern the propagation of ultrashort optical pulses in a long-haul telecommunication fiber. In terms of the exact rational solutions, we demonstrate several interesting rogue wave dynamics such as rogue wave doublets, quartets and sextets. The modulation instability responsible for the excitation of rogue waves from an unstable continuous background in such a complex nonlinear system is also discussed.

Optical soliton molecules of Lakshmanan–Porsezian–Daniel model in birefringent fibers by trial equation technique

This paper studies optical solitons with Lakshmanan–Porsezian–Daniel equation in birefringent fibers by trial equation methodology. These solitons are bright soliton, dark soliton, singular soliton that are quite well known as optical soliton molecules or pulses in the literature.

Optical solitons for Lakshmanan–Porsezian–Daniel model by Riccati equation approach

Optical soliton solutions are retrieved for Lakshmanan–Porsezian–Daniel equation by employing Riccati equation approach. The soiton solutions that are presented are generalized versions of solutions that have been reported in the past. The constraint conditions guarantee the existence of such solitons.

M-derivative applied to the soliton solutions for the Lakshmanan–Porsezian–Daniel equation with dual-dispersion for optical fibers

Optical dispersive soliton solutions for the fractional Lakshmanan–Porsezian–Daniel equation for optical fibers are studied in this paper considering the M-derivative of order $$\chi$$ . The analytical method considered here is based on the Jacobi elliptic function (JEF) anzatz method. We found new optical soliton solutions that are relevant for the dynamics inside optical fibers. Some constraints conditions arise between the parameters of the JEF soliton solutions. Typical behaviour of the soliton solutions obtained is depicted in some interesting simulations.

Optimal control for soliton breathers of the Lakshmanan–Porsezian–Daniel, Hirota, and cmKdV models

We apply the method for systematic construction of the two-soliton (and in principal, N-soliton) breather solutions on the zero background to the Lakshmanan–Porsezian–Daniel model with varying dispersion and nonlinearity, gain or loss, and derive the specific conditions for the appearance of the so-called standing and moving soliton breathers. We show that both all parameters of constituent solitons forming the breather and the varying dispersion and nonlinearities should be appropriately chosen in accordance with the exact integrability conditions of the Lakshmanan–Porsezian–Daniel equation with vanishing boundary conditions. We compare the details of periodic breather dynamics for the complex modified KdV, Hirota, and Lakshmanan–Porsezian–Daniel models with the classical Satsuma–Yajima breather behavior. We derive simple formulas for the soliton breather periods and use them to understand the possibilities to control breather dynamics, and, in particular, to realize the so-called regimes of “artificial breathing”, when periods of soliton breathing in space and time are controlled by choosing appropriate complex spectral parameters defining the amplitudes and velocities of constituent solitons. Of fundamental importance is the remarkable theoretical fact that the higher-order nonlinear and dispersion effects included into (or removed from) the new higher-order equations of the AKNS hierarchy, as a rule, do not destroy soliton breathers discovered here and do not transform them into dispersive waves. On the contrary, we demonstrate that novel and novel soliton breathers can appear in the framework of the next, more and more higher orders of the AKNS and NLSE hierarchies.

Optical solitons in birefringent fibers for Lakshmanan–Porsezian–Daniel model by extended Jacobi's elliptic function expansion scheme

This paper integrates the vector coupled Lakshmanan–Porsezian–Daniel equation in birefringent fibers by the aid of extended Jacobi's elliptic function expansion scheme. Jacobi doubly periodic wave solutions are retrieved. The solutions derived by this integration mechanism, in the limiting case, gives rise to dark solitons or singular solitons or periodic solutions.

Optical solitons in birefringent fibers for Lakshmanan–Porsezian–Daniel model using exp(−ϕ(ξ))-expansion method

This paper studies optical solitons in birefringent fibers by the aid of exp-function approach. The model that is analyzed is Lakshmanan–Porsezian–Daniel equation which is first written in two-component form for vector solitons. The integrability criteria are also presented in the paper.

Optical solitons with Lakshmanan–Porsezian–Daniel model using a couple of integration schemes

This paper retrieves dark and singular optical soliton solutions to the Lakshmanan–Porsezian–Daniel equation for Kerr law nonlinearity by using two integration schemes. These are extended Jacobi's elliptic function approach and exp(−Φ(η))–expansion method. The existence criteria for these solitons are also obtained that are presented as constraint conditions. As a byproduct, periodic singular solutions are recovered and these too are listed in the paper.

Dynamical Behavior of Solution in Integrable Nonlocal Lakshmanan—Porsezian—Daniel Equation**Supported by the National Natural Science Foundation of China under Grant No. 11271210 and the K.C. Wong Magna Fund in Ningbo University

The integrable nonlocal Lakshmanan—Porsezian—Daniel (LPD) equation which has the higher-order terms (dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation, provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed.