Application of new Kudryashov method to various nonlinear partial differential equations

• Published in: Optical and quantum electronics Vol. 55; no. 1
• Main Authors: Malik, Sandeep, Hashemi, Mir Sajjad, Kumar, Sachin, Rezazadeh, Hadi, Mahmoud, W., Osman, M. S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2023; Springer Nature B.V
• Subjects: Boussinesq equations; Characterization and Evaluation of Materials; Computer Communication Networks; Electrical Engineering; Exact solutions; Lasers; Nonlinear differential equations; Optical Devices; Optics; Partial differential equations; Photonics; Physics; Physics and Astronomy; Solitary waves; New Kudryashov method; Boussinesq equation; Klein–Gordon equation; Kadomtsev–Petviashvili equation; Exact solutions
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-022-04261-y

The purpose of this work is to seek various innovative exact solutions using the new Kudryashov approach to the nonlinear partial differential equations (NLPDEs). This technique obtains novel exact solutions of soliton types. Moreover, several 3D and 2D plots of the higher dimensional Klein-Gordon, Kadomtsev-Petviashvili, and Boussinesq equations are demonstrated by considering the relevant values of the aforementioned parameters to exhibit the nonlinear wave structures more adequately. The new Kudryashov technique is an effective, and simple technique that provides new generalized solitonic wave profiles. It is anticipated that these novel solutions will enable a thorough understanding of the development and dynamic nature of such models.