Scientific Source Codes
(Published Articles)
Symbolic Techniques
Wave Transformational Methods
Lie Symmetry Analysis
Painlevé Analysis
Symbolic Techniques
DSA: Direct Symbolic Approach,
SBT: Symbolic Bilinear Technique,
HBT: Hirota Bilinear Technique,
SCA: Symbolic Computational Approach,
HBFA: Hirota Bilinear Form Algorithm.
PA: Painlevé Analysis
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​2025 (HBT, DSA, PA) On investigation of kink-solitons and rogue waves to a new integrable (3+1)-dimensional KdV-type generalized equation in nonlinear sciences, Nonlinear Dynamics, 113:10261–10276, Q1, IF:5.6, SCIE.
Publication: Link
Paper Preprint: PDF
Kink Solitons: Mathematica Code
Rogue Waves: Mathematica Code
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2025 (HBT, DSA) Painleve analysis, restricted bright-dark N-solitons, and N-rogue waves of a (4+1)-dimensional variable-coefficient generalized KP equation in nonlinear sciences, Nonlinear Dynamics, 112:11373-11382, Q1, IF:5.6, SCIE.
Publication: Link
Paper Preprint: PDF
Bright-Dark Solitons: Mathematica Code
Rogue Waves: Mathematica Code
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2024 (DSC) Rogue-wave structures for a generalized (3+1)-dimensional nonlinear wave equation in liquid with gas bubbles, Physica Scripta, 99:105291, Q2, IF: 2.6, SCIE.
Publication: Link
Paper Preprint: PDF
Rogue Waves: Mathematica Code
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2024 (SBT) Generalization and analytic exploration of soliton solutions for nonlinear evolution equations via a novel symbolic approach in fluids and nonlinear sciences, Chinese Journal of Physics, 92:10-21, Q2, IF:4.6, SCIE.
Publication: Link
Paper Preprint: PDF
KdV Equation Solitons: Mathematica Code
KP Equation Solitons: Mathematics Code
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2024 (DSA) Bilinearization and new center-controlled N-rogue solutions to a (3+1)-dimensional generalized KdV-type equation in plasmas via direct symbolic approach, Nonlinear Dynamics, 112:11373-11382, Q1, IF:5.6, SCIE.
Publication: Link
Paper Preprint: PDF
Center-controlled Rogue Waves: Mathematica Code
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2023 (DSA) A novel analysis of Cole-Hopf transformations in different dimensions, solitons, and rogue waves for a (2 + 1)-dimensional shallow water wave equation of ion-acoustic waves in plasmas, Physics of Fluids, 35:127128, Q1, IF:4.6, SCIE.
Publication: Link
Paper Preprint: PDF
Cole-Hopf Transformations: Mathematica Code
Rogue Waves: Mathematica Code
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2023 (DSA, HBT, PA) Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves, Nonlinear Dynamics, 111:20275–20288, Q1, IF:5.6, SCIE.
Publication: Link
Paper Preprint: PDF
Rogue Waves: Mathematica Code
Dispersive Solitons: Mathematica Code
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2023 (SCA, HBT) Newly formed center-controlled rogue wave and lump solutions of a generalized (3+1)-dimensional KdV-BBM equation via symbolic computation approach, Physica Scripta, 98(8):085237, Q2, IF: 2.9, SCIE.
Publication: Link
Paper Preprint: PDF
Rogue Waves & Lumps: Mathematica Code
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2023 (DSA Design, PA) A direct symbolic computation of center-controlled rogue waves to a new Painlevé-integrable (3+1)-D generalized nonlinear evolution equation in plasmas, Nonlinear Dynamics, 111:16395–16405, Q1, IF: 5.7, SCIE.
Publication: Link
Paper Preprint: PDF
Center-controlled Rogue Waves: Mathematica Code
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2022 (PA, HBT) A generalized nonlinear fifth-order KdV-type equation with multiple soliton solutions: Painlevé analysis and Hirota Bilinear technique, Physica Scripta, 97(12):125214, Q2, IF: 3.1, SCIE
Publication: Link
Paper Preprint: PDF
Soliton Solutions: Mathematica Code -
2022 (HBT) Application of Hirota’s Direct Method to Nonlinear Partial Differential Equations: Bilinear Form and Soliton Solutions, Hans Shodh Sudha, 3(2):31-38.
Publication: Link
Paper Preprint: PDF
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2022 (HBT) Lump, soliton, and interaction solutions to a generalized two-mode higher-order nonlinear evolution in plasma physics, Nonlinear Dynamics, 110:693-704, Q1, IF: 5.7, SCIE.
Publication: Link
Paper Preprint: PDF
Soliton Solutions: Mathematica Code
Lump Solutions: Mathematica Code
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2022 (HBFA) A novel and efficient method for obtaining Hirota's bilinear form for the nonlinear evolution equation in (n+1) dimensions, Partial Differential Equations in Applied Mathematics, 5:100274, SCOPUS.
Publication: Link
Paper Preprint: PDF
Bilinear Forms: Mathematica Code
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2022 (PA, HBT) Generalized fifth-order nonlinear evolution equation for the Sawada-Kotera, Lax, and Caudrey-Dodd-Gibbon equations in plasma physics: Painlevé analysis and multi-soliton solutions, Physica Scripta, 97(3):035201, Q2, IF: 3.1, SCIE.
Publication: Link
Paper Preprint: PDF
Soliton Solutions: Mathematica Code -
2021 (HBT) A study of multi-soliton solutions, breathers, lumps, and their interactions for Kadomtsev-Petviashvili equation with variable time coefficient using Hirota method, Physica Scripta, 96(12):125255, Q2, IF: 3.1, SCIE.
Publication: Link
Paper Preprint: PDF
Soliton, Rogue & Lump Solutions: Mathematica Code
Wave Transformational Methods
GERFM: Generalized Exponential Rational Function Method
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​2025 (GERFM) Novel exploration of nonlinear waves of a generalized (2+1)-dimensional extended Boussinesq equation: solitons, breathers and periodic background waves, Journal of Applied Mathematics and Symbolic Science, 1(1):14–26.
Publication: Link
Nonlinear Waves: Mathematica Code​
Lie Symmetry Analysis
Lie Symmetry Reduction
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Coming soon...
Painlevé Analysis
Integrability Test
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Coming soon...

