Retrieval of diverse soliton, lump solutions to a dynamical system of the nonlinear (\(4+1\)) Fokas equation and stability analysis

• Adeyemo, O.D., Khalique, C.M.: Analytic solutions and conservation laws of a (2+ 1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation. Chin. J. Phys. 77, 927–944 (2022)

  Article  MathSciNet  Google Scholar 

• Ahmad, J., Akram, S., Ali, A.: Analysis of new soliton type solutions to generalized extended (2+ 1)-dimensional Kadomtsev–Petviashvili equation via two techniques. Ain Shams Eng. J. 1-15 (2023)

• Ahmad, J., Akram, S., Rehman, S.U., Turki, N.B., Shah, N.A.: Description of soliton and lump solutions to \(M\)-truncated stochastic Biswas–Arshad model in optical communication. Results Phys. 51, 1–17 (2023)

• Ahmad, J., Akram, S., Noor, K., Nadeem, M., Bucur, A., Alsayaad, Y.: Soliton solutions of fractional extended nonlinear Schrödinger equation arising in plasma physics and nonlinear optical fiber. Sci. Rep. 13, 10877 (2023)

  Article  ADS  Google Scholar 

• Akinyemi, L., Morazara, E.: Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev-Petviashvili equation. Nonlinear Dyn. 1–25 (2022)

• Akram, G., Sadaf, M., Khan, M.A.U.: Dynamics investigation of the (4+1)-dimensional Fokas equation using two effective techniques. Results Phys. 42, 105994 (2022)

  Article  Google Scholar 

• Akram, S., Ahmad, J., Rehman, S.U., Sarwar, S., Ali, A.: Dynamics of soliton solutions in optical fibers modelled by perturbed nonlinear Schrödinger equation and stability analysis. Opt. Quant. Electron. 55, 450 (2023)

  Google Scholar 

• Akram, S., Ahmad, J., Rehman, S.U.: Stability analysis and dynamical behavior of solitons in nonlinear optics modelled by Lakshmanan–Porsezian–Daniel equation. Opt. Quantum Electron. 55, 685 (2023)

  Google Scholar 

• Akram, S., Ahmad, J., Rehman, S.U., Younas, T.: Stability analysis and dispersive optical solitons of fractional Schrödinger–Hirota equation. Opt. Quantum Electron. 55, 664 (2023)

  Google Scholar 

• Al Qarni, A.A., Bodaqah, A.M., Mohammed, A.S.H.F., Alshaery, A.A., Bakodah, H.O., Biswas, A.: Dark and singular cubic-quartic optical solitons with Lakshmanan–Porsezian–Daniel equation by the improved Adomian decomposition scheme. Ukr. J. Phys. Opt. 24, 46–61 (2023)

  Article  Google Scholar 

• Alam, M.N.: Soliton solutions to the electric signals in telegraph lines on the basis of the tunnel diode. Partial Differ. Equ. Appl. 7, 100491 (2023)

  ADS  Google Scholar 

• Ali, A., Ahmad, J., Javed, S.: Solitary wave solutions for the originating waves that propagate of the fractional Wazwaz–Benjamin–Bona–Mahony system. Alex. Eng. J. 69, 121–133 (2023)

  Article  Google Scholar 

• Alsallami, S.A., Rizvi, S.T., Seadawy, A.R.: Study of stochastic-fractional Drinfel’d–Sokolov–Wilson equation for \(M\)-shaped rational, homoclinic breather, periodic and kink-cross rational solutions. Mathematics 11, 1504 (2023)

  Article  Google Scholar 

• Chong, Y.D.: Complex Methods for the Sciences. Nanyang Technological University, MH2801 (2016)

• El-Sayed, Z.E.S.M., Al-Nowehy, A.G.: Exact traveling wave solutions for nonlinear PDEs in mathematical physics using the generalized Kudryashov method. Serb. J. Electr. Eng. 13, 203–227 (2016)

  Article  Google Scholar 

• Fendzi-Donfack, E., Tala-Tebue, E., Inc, M., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness. Opt. Quantum Electron. 55, 1–25 (2023)

  Article  Google Scholar 

• Fokas, A.S.: Integrable nonlinear evolution partial differential equations in 4+2 and 3+1 dimensions. Phys. Rev. Lett. 96, 190201 (2006)

  Article  MathSciNet  Google Scholar 

• Hong, B.: Abundant explicit solutions for the \(M\)-fractional coupled nonlinear Schrödinger–KdV equations. J. Low Freq. Noise Vib. Act. Control 42, 1–20 (2023)

• Jawad, A.J.A.M., Petković, M.D., Biswas, A.: Modified simple equation method for nonlinear evolution equations. Appl. Math. Comput. 217, 869–877 (2010)

• Jiang, Z., Zhang, Z.G., Li, J.J., Yang, H.W.: Analysis of Lie symmetries with conservation laws and solutions of generalized (4+1)-dimensional time-fractional Fokas equation. Fractal Fract 6, 108 (2022)

  Article  Google Scholar 

• Jisha, C.R., Dubey, R.K.: Wave interactions and structures of (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Nonlinear Dyn. 110, 3685–3697 (2022)

  Article  MATH  Google Scholar 

• Manafian, J., Ilhan, O.A., Alizadeh, A.A.: Periodic wave solutions and stability analysis for the KP-BBM equation with abundant novel interaction solutions. Phys. Scr. 95, 065203 (2020)

  Article  Google Scholar 

• Mohammed, W.W., Cesarano, C., Al-Askar, F.M.: Solutions to the (4+1)-dimensional time-fractional Fokas equation with M-truncated derivative. Mathematics 11, 194 (2022)

  Article  Google Scholar 

• Nandi, D.C., Ullah, M.S., Ali, M.Z: Application of the unified method to solve the ion sound and Langmuir waves model. Heliyon 8, 1–8 (2022)

• Osman, M.S., Tariq, K.U., Bekir, A., Elmoasry, A., Elazab, N.S., Younis, M., Abdel-Aty, M.: Investigation of soliton solutions with different wave structures to the (2+ 1)- dimensional Heisenberg ferromagnetic spin chain equation. Commun. Theor. Phys. 72, 035002 (2020)

  Article  MathSciNet  MATH  Google Scholar 

• Qian, X., Lu, D., Arshad, M., Shehzad, K.: Novel traveling wave solutions and stability analysis of perturbed Kaup–Newell Schrödinger dynamical model and its applications. Chin. Phys. B 30, 020201 (2021)

  Article  Google Scholar 

• Rani, M., Ahmed, N., Dragomir, S.S., Mohyud-Din, S.T: Traveling wave solutions of 3+ 1-dimensional Boiti–Leon–Manna–Pempinelli equation by using improved \(\tanh (\frac{\phi }{2})\)-expansion method. Partial Differ. Equ. Appl. 6, 1–8 (2023)

• Rehman, S.U., Ahmad, J.: Dispersive multiple lump solutions and soliton’s interaction to the nonlinear dynamical model and its stability analysis. Eur. Phys. J. D, 76, 1–13 (2022)

• Rehman, S.U., Ahmad, J.: Dynamics of optical and multiple lump solutions to the fractional coupled nonlinear Schrödinger equation. Opt. Quantum Electron. 54, 640 (2022)

  Google Scholar 

• Sarwar, S.: New soliton wave structures of nonlinear (4+ 1)-dimensional Fokas dynamical model by using different methods. Alex. Eng. J. 60, 795–803 (2021)

  Article  Google Scholar 

• Sarwar, S., Furati, K.M., Arshad, M.: Abundant wave solutions of conformable space-time fractional order Fokas wave model arising in physical sciences. Alex. Eng. J. 60, 2687–2696 (2021)

  Article  Google Scholar 

• Senol, M., Gencyigit, M., Sarwar, S.: Different solutions to the conformable generalized (3+ 1)-dimensional Camassa–Holm–Kadomtsev–Petviashvili equation arising in shallow water waves. Int. J. Geom. Methods Mod. Phys. https://doi.org/10.1142/S0219887823501542 (2023)

• Shahzad, T., Ahmad, M.O., Baber, M.Z., Ahmed, N., Ali, S.M., Akgül, A., Eldin, S.M.: Extraction of soliton for the confirmable time-fractional nonlinear Sobolev-type equations in semiconductor by \(\phi ^6\)-modal expansion method. Results Phys. 46, 106299 (2023)

  Article  Google Scholar 

• Shehzad, K., Zhenhua, T., Shoukat, S., Saeed, A., Ahmad, I., Sarwar Bhatti, S., Chelloug, S.A.: A deep-ensemble-learning-based approach for skin cancer diagnosis. Electronics 12, 1342 (2023)

  Article  Google Scholar 

• Tarla, S., Ali, K., Yilmazer, R., Osman, M.S.: On dynamical behavior for optical solitons sustained by the perturbed Chen–Lee–Liu model. Commun. Theor. Phys. 72, 075005 (2022)

  MATH  Google Scholar 

• Ullah, M.S., Roshid, H.O., Ma, W.X., Ali, M.Z., Rahman, Z.: Interaction phenomena among lump, periodic and kink wave solutions to a (3+ 1)-dimensional Sharma–Tasso–Olver-like equation. Chin. J. Phys. 68, 699–711 (2020)

  Article  MathSciNet  Google Scholar 

• Ullah, M.S., Ali, M.Z., Roshid, H.O., Hoque, M.F.: Collision phenomena among lump, periodic and stripe soliton solutions to a (2+ 1)-dimensional Benjamin–Bona–Mahony–Burgers Model. Eur. Phys. J. Plus 136, 1–9 (2021)

  Article  Google Scholar 

• Ullah, M.S., Abdeljabbar, A., Roshid, H.O., Ali, M.Z.: Application of the unified method to solve the Biswas–Arshed model. Results Phys. 42, 105946 (2022)

  Article  Google Scholar 

• Ullah, M.S., Alshammari, F.S., Ali, M.Z.: Collision phenomena among the solitons, periodic and Jacobi elliptic functions to a (3+ 1)-dimensional Sharma–Tasso–Olver-like model. Results Phys. 36, 105412 (2022)

  Article  Google Scholar 

• Ullah, M.S., Ahmed, O., Mahbub, M.A.: Collision phenomena between lump and kink wave solutions to a (3+1)-dimensional Jimbo–Miwa-like model. Partial Differ. Equ. Appl. 5, 100324 (2022)

  Google Scholar 

• Ullah, M.S., Seadawy, A.R., Ali, M.Z.: Optical soliton solutions to the Fokas–Lenells model applying the \(\phi ^{6}\)-model expansion approach. Opt. Quantum Electron. 55, 495 (2023)

  Article  Google Scholar 

• Ullah, M.S., Baleanu, D., Ali, M.Z.: Novel dynamics of the Zoomeron model via different analytical methods. Chaos Solitons Fractals 174, 113856 (2023)

• Ullah, M.S., Mostafa, M., Ali, M.Z., Roshid, H.O., Akter, M.: Soliton solutions for the Zoomeron model applying three analytical techniques. PLoS ONE 18, e0283594 (2023)

  Article  Google Scholar 

• Ullah, M.S., Ali, M.Z., Rezazadeh, H.: Kink and breather waves with and without singular solutions to the Zoomeron model. Results Phys. 49, 106535 (2023)

  Article  Google Scholar 

• Wazwaz, A.M., Alatawi, N.S., Albalawi, W., El-Tantawy, S.A.: Painlevé analysis for a new (3+ 1)-dimensional KP equation: Multiple-soliton and lump solutions. Europhys. Lett. 140, 1–6 (2022)

• Zhao, X., Pang, F., Gegen, H.: Interactions among two-dimensional nonlinear localized waves and periodic wave solution for a novel integrable \((2+ 1)\)-dimensional KdV equation. Nonlinear Dyn. 110, 3629–3654 (2022)

  Article  Google Scholar 

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