Extended Trial Function Method Research Articles

Singular and Bright soliton solutions for the coupled system corresponding to Gerdjikov-Ivanov equation with four-wave mixing terms

The extended trial function method is utilized in birefringent fibers to generate optical soliton solutions to the coupled system that correspond to the Gerdjikov-Ivanov equation with four-wave mixing terms. The approach yields singular and bright soliton solutions, and in addition extremely important singular and singular periodic soliton solutions are extracted by taken the limit of the modulus of ellipticity of the Jacobi’s elliptic function. The conditions under which the soliton solution exist are also provided.

Optical solitons in fiber Bragg gratings with dispersive reflectivity for quadratic–cubic nonlinearity by extended trial function method

This paper studies optical solitons in fiber Bragg gratings, that appear with quadratic–cubic nonlinearity, in presence of dispersive reflectivity. The extended trial function scheme revealed bright and singular optical soliton solutions to the model. The phase-matching condition was adopted to this model.

Optical solitons in fiber Bragg gratings with dispersive reflectivity for parabolic law nonlinearity by extended trial function method

This paper applies extended trial function scheme to retrieve bright and singular optical soliton solutions to fiber Bragg gratings that maintains parabolic law nonlinearity. The existence criteria for the solitons are presented. Additional solutions, such as rational waves and periodic solutions, naturally emerge from the scheme as a byproduct.

Solitons in optical fiber Bragg gratings with dispersive reflectivity by extended trial function method

This paper retrieves optical solitons in fiber Bragg gratings, with dispersive reflectivity, by extended trial function approach. Bright and singular soliton solutions are listed and the corresponding integrability conditions are also enumerated.

Optical solitons in (2+1)–Dimensions with Kundu–Mukherjee–Naskar equation by extended trial function scheme

This paper addresses Kundu–Mukherjee–Naskar equation by the aid of extended trial function method to recover optical soliton solutions in (2+1)–dimensions. The integration algorithm revealed doubly periodic functions. Upon taking the limiting values of the modulus of ellipticity, bright and singular solitons as well as singular periodic solutions emerge. Additional solutions such as plane waves also fall out of the scheme.

Optical soliton perturbation with full nonlinearity by extended trial function method

The extended trial function scheme is applied to retrieve soliton solutions to the perturbed nonlinear Schrodinger’s equation with ten forms of fiber nonlinearity. Bright, dark and singular soliton solutions are retrieved that appear with their respective existence criteria. Some additional forms of nonlinear waves naturally emerge as a byproduct of the integration scheme.

Optical solitons and conservation law in birefringent fibers with Kundu–Eckhaus equation by extended trial function method

This paper presents bright and singular optical solitons in birefringent fibers modeled by Kundu–Eckhaus equation. The extended trial function scheme successfully obtains such solitons. The conservation law is also computed for the bright solitons.

Optical solitons with Biswas-Arshed equation by extended trial function method

This paper studies soliton dynamics for Biswas-Arshed model that is considered when group velocity dispersion is negligibly small and self-phase modulation is totally absent. Two nonlinear forms for the model are studied by the aid of extended trial function scheme. Bright, dark and singular soliton solutions emerge from this scheme.

Stationary optical solitons with nonlinear group velocity dispersion by extended trial function scheme

This paper applies extended trial function method to obtain stationary optical soliton solutions when group velocity dispersion is nonlinear. There are four forms of nonlinear media that are studied in this paper.

Optical solitons with differential group delay and dual-dispersion for Lakshmanan–Porsezian–Daniel model by extended trial function method

This paper employs extended trial function method to extract soliton solutions to the vector-coupled Lakshmanan–Porsezian–Daniel model in birefringent fibers. The existence of these solitons is guaranteed with the integrability criteria that are also presented.

Dispersive optical solitons with differential group delay and parabolic law nonlinearity by extended trial function method

This paper obtains bright and singular dispersive optical solitons for birefringent fibers in a parabolic law medium. The extended trial function algorithm was implemented to extract these soliton solutions. In addition, cnoidal and snoidal wave solutions are also recovered for the model.

Optical soliton for perturbed nonlinear fractional Schrödinger equation by extended trial function method

This paper retrieves, bright, dark and singular optical solitons with the help of extended trial equation scheme. We consider Kerr law, power law and log law of nonlinearity. We find the solutions in terms of Jacobi elliptic functions and in the limiting cases of the modulus of ellipticity.

Sub-pico-second chirped optical solitons in mono-mode fibers with Kaup–Newell equation by extended trial function method

This paper employs extended trial function method to retrieve sub-pico-second optical soliton solutions to Kaup–Newell's equation that is one of the forms of derivative nonlinear Schrödinger's equation. Bright and singular soliton solutions are revealed with this algorithm.

Optical solitons with differential group delay and weak non-local nonlinearity by extended trial function method

This paper studies optical soliton solutions with differential group delay and non-local nonlinearity. The extended trial function approach retrieves bright and singular soliton solutions to the model. The existence criteria for these solitons are also given.

Optical solitons with differential group delay for coupled Fokas–Lenells equation by extended trial function scheme

This paper retrieves optical soliton solutions to the Fokas–Lenells equation in birefringent fibers by the application of extended trial function method. The algorithm reveals bright and singular soliton solutions to the model along with several other solutions whose limiting case for the modulus of ellipticity yields soliton solutions.

Optical solitons in parabolic law medium with weak non-local nonlinearity by extended trial function method

This paper retrieves optical soliton solutions in a parabolic law medium that also comes with weak nonlocal nonlinearity. The extended trial function method secures bright and singular soliton solutions to the model. In addition, plane waves and snoidal wave solutions also emerge naturally from this integration scheme.

Chirped solitons in optical metamaterials with parabolic law nonlinearity by extended trial function method

This paper secures chirped bright and singular soliton solutions in an optical metamaterial that is considered with parabolic law nonlinearity and self-steepening effect. The extended trial function method is the integration scheme adopted in this paper. Several other solutions such as singular periodic waves and elliptic functions naturally emerge as a byproduct of this scheme.

Resonant optical soliton perturbation with anti-cubic nonlinearity by extended trial function method

This paper studies the resonant optical solitons that comes with anti-cubic nonlinearity in presence of Hamiltonian perturbation terms. The extended trial function method is employed to retrieve cnoidal waves, bright and singular soliton solutions as well as periodic singular solutions to the model.

Solitons in magneto-optic waveguides by extended trial function scheme

This paper obtains soliton solutions to magneto-optic waveguides that appear with Kerr, power and log-law nonlinearities. The extended trial function method is employed to obtain these solutions. Thus, bright, dark and singular soliton solutions are retrieved. In addition, Gaussons are obtained for log-law nonlinear waveguides. All of these solutions appear with constraints that guarantees the existence of solitons and Gaussons.

Optical solitons in birefringent fibers by extended trial equation method

This paper studies solitons in optical fibers by the aid of extended trial function method. This powerful mathematical tool is applied to birefringent fibers with Kerr and parabolic laws of nonlinearity. Bright and singular soliton solutions are obtained along with respective constraints that must hold to guarantee the existence of these solitons. As a byproduct, singular periodic and doubly periodic solutions are also recovered from this algorithm.