Search results

The purpose of this paper is to introduce two new Painlevé-integrable extended Sakovich equations with (2 + 1) and (3 + 1) dimensions. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models.

The newly developed Sakovich equations have been handled by using the Hirota’s direct method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions.

The developed extended Sakovich models exhibit complete integrability in analogy with the original Sakovich equation.

This paper is to address these two main motivations: the study of the integrability features and solitons solutions for the developed methods.

This paper introduces two Painlevé-integrable extended Sakovich equations which give real and complex soliton solutions.

This paper presents useful algorithms for constructing new integrable equations and for handling these equations.

This paper gives two Painlevé-integrable extended equations which belong to second-order PDEs. The two developed models do not contain the dispersion term u_xxx. This paper presents an original work with newly developed integrable equations and shows useful findings.

This paper aims to develop a new (3 + 1)-dimensional Painlevée-integrable extended Sakovich equation. This paper formally derives multiple soliton solutions for this developed model.

This paper uses the simplified Hirota’s method for deriving multiple soliton solutions.

This paper finds that the developed (3 + 1)-dimensional Sakovich model exhibits complete integrability in analogy with the standard Sakovich equation.

This paper addresses the integrability features of this model via using the Painlevée analysis. This paper reports multiple soliton solutions for this equation by using the simplified Hirota’s method.

The study reports three non-linear terms added to the standard Sakovich equation.

The study presents useful algorithms for constructing new integrable equations and for handling these equations.

The paper reports a new Painlevée-integrable extended Sakovich equation, which belongs to second-order partial differential equations. The constructed model does not contain any dispersion term such as uxxx.

The purpose of this paper is to concern with introducing symmetry analysis to the extended Sakovich equation.

The newly developed Sakovich equation has been handled by using the Lie symmetries via using the Lie group method.

The developed extended Sakovich model exhibit symmetries and invariant solutions.

The present study is to address the two main motivations: the study of symmetry analysis and the study of soliton solutions of the extended Sakovich equation.

The work introduces symmetry analysis to the Painlevé-integrable extended Sakovich equation.

The work presents useful symmetry algorithms for handling new integrable equations.

The paper presents an original work with symmetry analysis and shows useful findings.

This study aims to develop two integrable shallow water wave equations, of higher-dimensions, and with constant and time-dependent coefficients, respectively. The author derives multiple soliton solutions and a class of lump solutions which are rationally localized in all directions in space.

The author uses the simplified Hirota’s method and lump technique for determining multiple soliton solutions and lump solutions as well. The author shows that the developed (2+1)- and (3+1)-dimensional models are completely integrable in in the Painlené sense.

The paper reports new Painlevé-integrable extended equations which belong to the shallow water wave medium.

The author addresses the integrability features of this model via using the Painlevé analysis. The author reports multiple soliton solutions for this equation by using the simplified Hirota’s method.

The obtained lump solutions include free parameters; some parameters are related to the translation invariance and the other parameters satisfy a non-zero determinant condition.

The work presents useful algorithms for constructing new integrable equations and for the determination of lump solutions.

The paper presents an original work with newly developed integrable equations and shows useful findings of solitary waves and lump solutions.

This study aims to develop a new (3 + 1)-dimensional Painlevé-integrable extended Vakhnenko–Parkes equation. The author formally derives multiple soliton solutions for this developed model.

The study used the simplified Hirota’s method for deriving multiple soliton solutions.

The study finds that the developed (3 + 1)-dimensional Vakhnenko–Parkes model exhibits complete integrability in analogy with the standard Vakhnenko–Parkes equation.

This study addresses the integrability features of this model via using the Painlevé analysis. The study also reports multiple soliton solutions for this equation by using the simplified Hirota’s method.

The work reports extension of the (1 + 1)-dimensional standard equation to a (3 + 1)-dimensional model.

The work presents useful algorithms for constructing new integrable equations and for handling these equations.

The paper presents an original work with newly developed integrable equation and shows useful findings.

This paper aims to introduce a new (3 + 1)-dimensional fourth-order integrable equation characterized by second-order derivative in time t. The new equation models both right- and left-going waves in a like manner to the Boussinesq equation.

This formally uses the simplified Hirota’s method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space.

This paper confirms the complete integrability of the newly developed (3 + 1)-dimensional model in the Painevé sense.

This paper addresses the integrability features of this model via using the Painlevé analysis.

This paper presents a variety of lump solutions via using a variety of numerical values of the included parameters.

This work formally furnishes useful algorithms for extending integrable equations and for the determination of lump solutions.

To the best of the author’s knowledge, this paper introduces an original work with newly developed integrable equation and shows useful findings of solitons and lump solutions.

This study aims to explore novel solitary wave solutions of a new (3 + 1)-dimensional nonlocal Boussinesq equation that illustrates nonlinear water dynamics.

The authors use the Painlevé analysis to study its complete integrability in the Painlevé sense.

The Painlevé analysis demonstrates the compatibility condition for the model integrability with the addition of new extra terms.

The phase shifts, phase variables and Hirota’s bilinear algorithm are used to furnish multiple soliton solutions.

The authors also furnish a variety of numerous periodic solutions, kink solutions and singular solutions.

The work formally furnishes algorithms for investigating several physical systems, including plasma physics, optical communications and oceans and seas, among others.

This paper presents an original work using a newly developed Painlevé integrable model, as well as novel and insightful findings.

This study aims to introduce a variety of integrable Boussinesq equations with distinct dimensions.

The author formally uses the simplified Hirota’s method and lump schemes for exploring lump solutions, which are rationally localized in all directions in space.

The author confirms the lump solutions for every model illustrated by some graphical representations.

The author examines the features of the obtained lumps solutions.

The author presents a variety of lump solutions via using a variety of numerical values of the included parameters.

This study formally furnishes useful algorithms for using symbolic computation with Maple for the determination of lump solutions.

This paper introduces an original work with newly useful findings of lump solutions.

This study aims to explore a novel model that integrates the Kairat-II equation and Kairat-X equation (K-XE), denoted as the Kairat-II-X (K-II-X) equation. This model demonstrates the connections between the differential geometry of curves and the concept of equivalence.

The Painlevé analysis shows that the combined K-II-X equation retains the complete Painlevé integrability.

This study explores multiple soliton (solutions in the form of kink solutions with entirely new dispersion relations and phase shifts.

Hirota’s bilinear technique is used to provide these novel solutions.

This study also provides a diverse range of solutions for the K-II-X equation, including kink, periodic and singular solutions.

This study provides formal procedures for analyzing recently developed systems that investigate optical communications, plasma physics, oceans and seas, fluid mechanics and the differential geometry of curves, among other topics.

The study introduces a novel Painlevé integrable model that has been constructed and delivers valuable discoveries.

This study aims to investigate two newly developed (3 + 1)-dimensional Kairat-II and Kairat-X equations that illustrate relations with the differential geometry of curves and equivalence aspects.

The Painlevé analysis confirms the complete integrability of both Kairat-II and Kairat-X equations.

This study explores multiple soliton solutions for the two examined models. Moreover, the author showed that only Kairat-X give lump solutions and breather wave solutions.

The Hirota’s bilinear algorithm is used to furnish a variety of solitonic solutions with useful physical structures.

This study also furnishes a variety of numerous periodic solutions, kink solutions and singular solutions for Kairat-II equation. In addition, lump solutions and breather wave solutions were achieved from Kairat-X model.

The work formally furnishes algorithms for studying newly constructed systems that examine plasma physics, optical communications, oceans and seas and the differential geometry of curves, among others.

This paper presents an original work that presents two newly developed Painlev\'{e} integrable models with insightful findings.