New optical solitons for the Volterra lattice system using the generalized exponential rational function approach
Samira Heidarisamira_heidari178@yahoo.comDepartment of Applied Mathematics Faculty of Mathematical Sciences University of Mazandaran P. O. Box 416Babolsar, IranView full profile → , *Mostafa EslamiCorresponding authorMostafa.eslami@umz.ac.irDepartment of Applied Mathematics Faculty of Mathematical Sciences University of Mazandaran P. O. Box 416Babolsar, IranView full profile →
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- Received:
- 01 Jul 2023
- Published Online:
- 02 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2096
- Pages:
- 1–13
Abstract
Keywords
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References
[1] N. Anwar, M. Raja, I. Ahmad, and A. K. Kiani, “Investigating differential difference equations: an in-depth review,” Journal of Innovative Technology, vol. 6, no. 1, pp. 25-39 (2024).
[2] Y. B. Suris, “Miura transformations for toda-type integrable systems, with applications to the problem of integrable discretizations,” arXiv preprint solv-int/9902003 (1999).
[3] D. Baldwin, Ü. Göktaş, and W. Hereman, “Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations,” Computer Physics Communications, vol. 162, no. 3, pp. 203-217 (2004).
[4] M. Wadati, “Transformation theories for nonlinear discrete systems,” Progress of Theoretical Physics Supplement, vol. 59, pp. 36-63 (1976).
[5] Y. Suris, “Miura transformation for toda-type integrable system, with applications to the problem of integrable discretizations, fachbereich mathematik,” (1998).
[6] E. Y. . R. M. Taher RB, Naassi N, “Another approach for leslie model via linear difference equations,” Journal of Interdisciplinary Mathematics, vol. 24, no. 5, pp. 1321-1345 (2021).
[7] K. S. Nasar and R. S. Fadhl, “Oscillation and nonoscillation criteria for second order half-linear neutral difference equations,” Journal of Interdisciplinary Mathematics, vol. 25, no. 5, pp. 1525-1533 (2022).
[8] E. Fermi, J. Pasta, and S. Ulam, “Collected works of enrico fermi,” University of Chicago Press, Chicago (1965).
[9] İ. Aslan, “The ablowitz-ladik lattice system by means of the extended (g¢/=g)-expansion method,” Applied Mathematics and Computation, vol. 216, no. 9, pp. 2778-2782 (2010).
[10] Y. B. Suris and O. Ragnisco, “What is the relativistic volterra lattice?” Communications in mathematical physics, vol. 200, pp. 445-485 (1999).
[11] N. Matsuura, “Discrete kdv and discrete modied kdv equations arising from motions of planar discrete curves,” International Mathematics Research Notices, vol. 2012, no. 8, pp. 1681-1698 (2012).
[12] W. X. Ma and Y. You, “Rational solutions of the toda lattice equation in casoratian form,” Chaos, Solitons & Fractals, vol. 22, no. 2, pp. 395- 406 (2004).
[13] D.-J. Ding, D.-Q. Jin, and C.-Q. Dai, “Analytical solutions of differential-difference sine-gordon equation,” Thermal Science, vol. 21, no. 4, pp. 1701-1705 (2017).
[14] C. U. Maheswari and M. Yogeshwaran, “Variable separable method and exact solutions of nonlinear partial differential, differential-difference and partial difference equations,” Indian Journal of Pure and Applied Mathematics, pp. 1-14 (2025).
[15] F. Xie, Z. Lu, and D. Wang, “The solutions of toda lattice and volterra lattice,” Chaos, Solitons and Fractals, vol. 27, pp. 217-222, 2006.
[16] M. S. Osman and B. Ghanbari, “New optical solitary wave solutions of fokas-lenells equation in presence of perturbation terms by a novel approach,” Optik, vol. 175, pp. 328-333, 12 (2018).
[17] H. Triki, M. Mirzazadeh, H. M. Ahmed, I. Samir, and M. S. Hashemi, “Higher-order sasasatsuma equation: Nuccis reduction and soliton solutions,” The European Physical Journal Plus 2023 138:5, vol. 138, pp. 1-10, 5 (2023).
[18] Y. Asghari, M. Eslami, and H. Rezazadeh, “Exact solutions to the conformable time-fractional discretized mkdv lattice system using the fractional transformation method,” Optical and Quantum Electronics, vol. 55, pp. 1-20 (2023).
[19] M. Y.Asghari and H. Rezazadeh, “Soliton solutions for the time- fractional nonlinear differential-difference equation with conformable derivatives in the ferroelectric materials,” Optical and Quantum Electronics, vol. 55, pp. 1-17 (2023).
[20] K. Hosseini, E. Hincal, M. Mirzazadeh, S. Salahshour, O. A. Obi, and F. Rabiei, “A nonlinear schrdinger equation including the parabolic law and its dark solitons,” Optik, vol. 273, 2 (2023).
[21] A.-M. Wazwaz and G.-Q. Xu, “Variety of optical solitons for perturbed fokaslenells equation through modied exponential rational function method and other distinct schemes,” Optik, p. 171011, 6 (2023).
[22] M. Y. Wang, A. Biswas, Y. Yldrm, H. M. Alshehri, L. Moraru, and S. Moldovanu, “Optical solitons in ber bragg gratings with dispersive re ectivity having ve nonlinear forms of refractive index,” Axioms, vol. 11, 11 (2022).
[23] Y. Zhang, J. Zhang, and R. Liu, “Magnetic eld analytical model for magnetic harmonic gears using the fractional linear transformation method,” Chinese J. Electr. Eng., vol. 5, no. 1, pp. 47-52 (2019).
[24] A. Houwe, M. Inc, S. Y. Doka, B. Acay, and L. V. Hoan, “The discrete tanh method for solving the nonlinear differential-difference equations,” Int. J. Mod. Phys. B, vol. 34, no. 19 (2020).
[25] B. Ghanbari and M. Inc, “A new generalized exponential rational function method to nd exact special solutions for the resonance nonlinear schrödinger equation,” The European Physical Journal Plus, vol. 133, no. 4, pp. 142-154 (2018).
[26] B. Ghanbari and J. Gomez-Aguilar, “The generalized exponential rational function method for radhakrishnan-kundu-lakshmanan equation with b-conformable time derivative,” Revista mexicana de fsica, vol. 65, no. 5, pp. 503-518 (2019).
[27] B. Ghanbari, “Abundant soliton solutions for the hirota-maccari equation via the generalized exponential rational function method,” Modern Physics Letters B, vol. 33, no. 09, p. 1950106 (2019).
[28] B. Ghanbari and K. S. Nisar, “Determining new soliton solutions for a generalized nonlinear evolution equation using an effective analytical method,” Alexandria Engineering Journal, vol. 59, no. 5, pp. 3171-3179 (2020).
[29] B. Ghanbari and C.-K. Kuo, “A variety of solitary wave solutions to the (2+ 1)-dimensional bidirectional sk and variable-coefficient sk equations,” Results in Physics, vol. 18, p. 103266 (2020).
[30] Y. Cao, F. Parvaneh, S. Alamri, A. A. Rajhi, and A. E. Anqi, “Some exact wave solutions to a variety of the schrödinger equation with two nonlinearity laws and conformable derivative,” Results in Physics, vol. 31, p. 104929 (2021).
[31] B. Günay, C.-K. Kuo, and W.-X. Ma, “An application of the exponential rational function method to exact solutions to the drinfeld-sokolov system,” Results in Physics, vol. 29, p. 104733 (2021).
[32] K. K. Ali, R. Yilmazer, H. Bulut, T. Aktürk, and M. Osman, “Abundant exact solutions to the strain wave equation in micro-structured solids,” Modern Physics Letters B, vol. 35, no. 26, p. 2150439 (2021).
