Search results

The purpose of this paper is concerned with developing a (2 + 1)-dimensional Benjamin–Ono equation. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for this equation.

The proposed model has been handled by using the Hirota’s method. Other techniques were used to obtain traveling wave solutions.

The examined extension of the Benjamin–Ono model features interesting results in propagation of waves and fluid flow.

The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple soliton solutions.

This work is entirely new and provides new findings, where although the new model gives multiple soliton solutions, it is nonintegrable.

The work develops two complete sets of multiple soliton solutions, the first set is real solitons, whereas the second set is complex solitons.

The purpose of this paper is concerned with developing two integrable Korteweg de-Vries (KdV) equations of third- and fifth-orders; each possesses time-dependent coefficients. The study shows that multiple soliton solutions exist and multiple complex soliton solutions exist for these two equations.

The integrability of each of the developed models has been confirmed by using the Painlev´e analysis. The author uses the complex forms of the simplified Hirota’s method to obtain two fundamentally different sets of solutions, multiple real and multiple complex soliton solutions for each model.

The time-dependent KdV equations feature interesting results in propagation of waves and fluid flow.

The paper presents a new efficient algorithm for constructing time-dependent integrable equations.

The author develops two time-dependent integrable KdV equations of third- and fifth-order. These models represent more specific data than the constant equations. The author showed that integrable equation gives real and complex soliton solutions.

The work presents useful findings in the propagation of waves.

The paper presents a new efficient algorithm for constructing time-dependent integrable equations.

The purpose of this paper is concerned with developing new integrable Vakhnenko–Parkes equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the time-dependent equations.

The developed time-dependent models have been handled by using the Hirota’s direct method. The author also uses Hirota’s complex criteria for deriving multiple complex soliton solutions.

The developed integrable models exhibit complete integrability for any analytic time-dependent coefficient.

The paper presents an efficient algorithm for handling time-dependent integrable equations with time-dependent coefficients.

The author develops two Vakhnenko–Parkes equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.

The work presents useful techniques for finding integrable equations with time-dependent coefficients.

The paper gives new integrable Vakhnenko–Parkes equations, which give a variety of multiple real and complex soliton solutions.

The purpose of this paper is to develop a new time-dependent KdV6 equation. The authors derive multiple soliton solutions and multiple complex soliton solutions for a time-dependent equation.

The newly developed time-dependent model has been handled by using the Hirota’s direct method. The authors also use the complex Hirota’s criteria for deriving multiple complex soliton solutions.

The examined extension of the KdV6 model exhibits complete integrability for any analytic time-dependent coefficient.

The paper presents a new efficient algorithm for constructing extended models which give a variety of multiple real and complex soliton solutions.

The paper introduced a new time-dependent KdV6 equation, where integrability is emphasized for any analytic time-dependent function.

The findings are new and promising. Multiple real and multiple complex soliton solutions were formally derived.

This is an entirely new work where a new time-dependent KdV6 equation is established. This is the first time that the KdV6 equation is examined as a time-dependent equation. Moreover, the complete integrability of this newly developed equation is emphasized via using Painlevé test.

The purpose of this paper is to introduce a variety of new completely integrable Calogero–Bogoyavlenskii–Schiff (CBS) equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for each of the developed models.

The newly developed models with time-dependent coefficients have been handled by using the simplified Hirota’s method. Moreover, multiple complex soliton solutions are derived by using complex Hirota’s criteria.

The developed models exhibit complete integrability, for specific determined functions, by investigating the compatibility conditions for each model.

The paper presents an efficient algorithm for handling integrable equations with analytic time-dependent coefficients.

The work presents new integrable equations with a variety of time-dependent coefficients. The author showed that integrable equations with time-dependent coefficients give real and complex soliton solutions.

This study presents useful algorithms for finding and studying integrable equations with time-dependent coefficients.

The paper gives new integrable CBS equations which appear in propagation of waves and provide a variety of multiple real and complex soliton solutions.

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.

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.

The purpose of this paper is concerned with investigating three integrable shallow water waves equations with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for these three models.

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

The developed integrable models exhibit complete integrability for any analytic time-dependent coefficients defined though compatibility conditions.

The paper presents an efficient algorithm for handling time-dependent integrable equations with analytic time-dependent coefficients.

This study introduces three new integrable shallow water waves equations with time-dependent coefficients. These models represent more specific data than the related equations with constant coefficients. The author shows that integrable equations with time-dependent coefficients give real and complex soliton solutions.

The paper presents useful algorithms for finding integrable equations with time-dependent coefficients.

The paper presents an original work with a variety of 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.

The purpose of this paper is to introduce two new (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli (BLMP) equations, the first with constant coefficients and the other with time-dependent coefficients. The author obtains multiple soliton solutions and multiple complex soliton solutions for the two developed models.

The newly developed models with constant coefficients and with time-dependent coefficients have been handled by using the simplified Hirota’s method. The author also uses the complex Hirota’s criteria for deriving multiple complex soliton solutions.

The two developed BLMP models exhibit complete integrability for any constant coefficient and any analytic time-dependent coefficients by investigating the compatibility conditions for each developed model.

The paper presents an efficient algorithm for handling integrable equations with constant and analytic time-dependent coefficients.

The paper presents two new integrable equations with a variety of coefficients. The author showed that integrable equations with constant and time-dependent coefficients give real and complex soliton solutions.

The paper presents useful algorithms for finding and studying integrable equations with constant and time-dependent coefficients.

The paper presents an original work with a variety of useful findings.