In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differen...

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. We demonstrate its integrability, provide its Lax pair, and, applying the Darboux transfromation, present its first and second order soliton solutions. The equation and its solutions have two free parameters. Setting one of these parameters to zero...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This integrable and admits Lax pair. The LPD generalization of nonlinear Schrodinger (NLS) described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using sine-cosine method hyperbolic tangent a variety new exact solutions are obtained. These methods effective tools for searching partial differential equations in mathemat...

In this study, some new exact travelling wave solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with Kerr law of nonlinearity are retrieved by complete discrimination system for polynomial method. Under transformation, LPD is reduced an ordinary differential equation. The including rational solutions, triangle function solitary and Jacobian elliptic obtained graphically illustrated us...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is studied. New analytical rational solitons to LPD are presented by an ansatz method. Wave solutions of three types, such as parabolic, trigonometric and hyperbolic function have been retrieved. All plotted in 3D enhance understanding their physical characteristics. These simulations, which represent behavior resulting hyperbolic, p...

In this article, we investigate novel optical solitons solutions for the Lakshmanan–Porsezian–Daniel (LPD) equation, along with group velocity dispersion and spatio-temporal dispersion, via three altered analytical techniques. A variety of bright, singular, dark, periodic kink are constructed Kudryashov method, generalized tanh method Sardar-subequation method. The dynamical behavior extracted ...

The inverse scattering transformation for a novel nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann–Hilbert problem. Firstly, integrable LPD corresponding to $$3\times 3$$ Lax pair proposed. Secondly, process left-right matrix Riemann–Hilbert(RH) problem constructed. analytical properties and symmetry relations Jost fun...

In this paper, we use the Riemann–Hilbert (RH) approach to examine integrable three-coupled Lakshmanan–Porsezian–Daniel (LPD) model, which describes dynamics of alpha helical protein with interspine coupling at fourth-order dispersion term. Through spectral analysis Lax pair, construct higher-order matrix RH problem for LPD when jump particular is a $$4\times 4$$ unit matrix, exact N-soliton so...

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation...

This paper seeks to find optical soliton solutions for Lakshmanan–Porsezian–Daniel (LPD) model with the parabolic law of nonlinearity. The spatiotemporal dispersion is included model, as it can contribute handling problem internet bottleneck. study was performed analytically using traveling wave hypothesis reduce an integrable form. Then, resulting equation handled two approaches, namely, auxil...