×

Modulated wave and modulation instability gain brought by the cross-phase modulation in birefringent fibers having anti-cubic nonlinearity. (English) Zbl 1496.81047

Summary: In this paper, we investigate the modulated wave and W-shaped profile in birefringent fibers having the anti-cubic nonlinearity terms. We use the traveling wave hypothesis to show out the velocity of the soliton and the constraint relation on the anti-cubic nonlinear terms. We use the Jacobi elliptic function solutions to point out two types of combined solutions. After some assumption on the modulus of the Jacobi elliptic function, we have shown out the combined bright-bright soliton and dark-dark soliton-like solutions. We use the linearizing algorithm to analyze the modulation instability (MI) growth rate. We have shown that the anti-cubic nonlinear terms and cross-phase modulation (XPM) can increase MI bands and the amplitude of the MI growth rate. To corroborate the prediction made on analytical results, we use the numerical investigation to show the propagation of the modulated wave and W-shaped profile in terms of cell index. We exhibited through the numerical results that the modulated wave can conserve high energy during its propagation in birefringent fibers. The obtained results will certainly open new perspectives in optical fibers during the transmission of huge data.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35C08 Soliton solutions
35C07 Traveling wave solutions
70H45 Constrained dynamics, Dirac’s theory of constraints
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
35A35 Theoretical approximation in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Tabi, C. B., Fractional unstable patterns of energy in α-helix proteins with long-range interactions, Chaos Solitons Fractals, 116, 386-391 (2018)
[2] Wazwaz, A. M., Bright and dark optical solitons for \((3 + 1)\)-dimensional Schrödinger equation with cubic-quintic-septic nonlinearities, Optik, 225, Article 165752 pp. (2021)
[3] Shukla, P. K.; Stenflo, L.; Fedele, R., Nonlinear effects caused by intense electromagnetic waves in an electron-positron-ion plasma, Phys. Plasmas, 10, 1, 310-313 (2003)
[4] Seadawy, A. R., Three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma, Comput. Math. Appl., 71, 1, 201-212 (2016) · Zbl 1443.82015
[5] Kudryashov, N. A., Quasi-exact solutions of the dissipative Kuramoto-Sivashinsky equation, Appl. Math. Comput., 219, 9245-9253 (2013) · Zbl 1297.35076
[6] Houwe, A.; Yakada, S.; Souleymanou, A.; Saliou, Y.; Inc, M.; Doka, S. Y., Survey of third- and fourth-order dispersions including ellipticity angle in birefringent fibers on W-shaped soliton solutions and modulation instability analysis, Eur. Phys. J. Plus, 136, 4, 1-27 (2021)
[7] Souleymanou, A.; Houwe, A.; Doka, S. Y.; Bouetou, T. B.; Inc, M.; Crepin, K. T., W-shaped profile and multiple optical soliton structure of the coupled nonlinear Schrödinger equation with the four-wave mixing term and modulation instability spectrum, Phys. Lett. A, 418, Article 127710 pp. (2021) · Zbl 07413633
[8] Ablowitz, M. J.; Horikis, T. P., Rogue waves in birefringent optical fibers: elliptical and isotropic fibers, J. Opt., 19, 6, Article 065501 pp. (2017)
[9] Souleymanou, A.; Ali, K. K.; Rezazadeh, H.; Eslami, M.; Mirzazadeh, M.; Korkmaz, A., The propagation of waves in thin-film ferroelectric materials, Pramana, 93, 2, 1-6 (2019)
[10] Biswas, A.; Mehmet, E.; Abdullah, S.; Milivoj, R. B., Optical solitons in birefringent fibers having anti-cubic nonlinearity with extended trial function, Optik, 185, 456-463 (2019)
[11] Biswas, A.; Mehmet, E.; Abdullah, S.; Milivoj, R. B., Optical solitons in birefringent fibers having anti-cubic nonlinearity with exp-function, Optik, 186, 363-368 (2019)
[12] Zayed, E. M.E.; Mohamed, E. M.A.; Biswas, A.; Mehmet, E.; Luminita, M.; Abdullah, K. A.; Milivoj, R. B., Dark, singular and straddled optical solitons in birefringent fibers with generalized anti-cubic nonlinearity, Phys. Lett. A, 384, Article 126417 pp. (2020) · Zbl 1448.35090
[13] Bölükbaşı, H.; Ekici, M.; Biswas, A., Optical solitons in birefringent fibers having anti-cubic nonlinearity with Jacobi’s elliptic function expansions, Opt. Quantum Electron., 53, 10, 1-36 (2021)
[14] Wazwaz, A. M., Optical bright and dark soliton solutions for coupled nonlinear Schrödinger (CNLS) equations by the variational iteration method, Optik, 207, Article 164457 pp. (2020)
[15] Issa, S.; Maïna, I.; Tabi, C. B.; Mohamadou, A.; Fouda, H. P.; Kofané, T. C., Long-range modulated wave patterns in certain nonlinear saturation alpha-helical proteins, Eur. Phys. J. Plus, 136, 9, 1-21 (2021)
[16] Zhang, L. H., Travelling wave solutions for the generalized Zakharov-Kuznetsov equation with higher-order nonlinear terms, Appl. Math. Comput., 208, 1, 144-155 (2009) · Zbl 1159.65351
[17] Eslami, M.; Hosseini, K.; Matinfar, M.; Mirzazadeh, M.; Ilie, M.; Gómez-Aguilar, J. F., A nonlinear Schrödinger equation describing the polarization mode and its chirped optical solitons, Opt. Quantum Electron., 53, 6, 1-9 (2021)
[18] Tala-Tebue, E.; Djoufack, Z. I.; Yamgoue, S. B.; Kenfack-Jiotsa, A.; Kofané, T. C., Chirped soliton solutions in optical medium, Opt. Quantum Electron., 51, 1, 1-16 (2019)
[19] Desaix, M.; Helczynski, L.; Anderson, D.; Lisak, M., Propagation properties of chirped soliton pulses in optical nonlinear Kerr media, Phys. Rev. E, 65, 5, Article 056602 pp. (2002)
[20] Susanto, H.; Malomed, B. A., Embedded solitons in second-harmonic-generating lattices, Chaos Solitons Fractals, 142, Article 110534 pp. (2021) · Zbl 1496.34030
[21] Rao, J.; Malomed, B. A.; Cheng, Y.; He, J., Dynamics of interaction between lumps and solitons in the Mel’nikov equation, Commun. Nonlinear Sci. Numer. Simul., 91, Article 105429 pp. (2020) · Zbl 1448.35437
[22] Tala-Tebue, E.; Korkmaz, A.; Rezazadeh, H.; Raza, N., New auxiliary equation approach to derive solutions of fractional resonant Schrödinger equation, Anal. Math. Phys., 11, 4, 1-13 (2021) · Zbl 1477.35247
[23] Biswas, A.; Yildirim, Y.; Yasar, E.; Zhou, Q.; Moshokoa, S. P.; Belic, M., Optical solitons for Lakshmanan-Porsezian-Daniel model by modified simple equation method, Optik, 160, 24-32 (2018)
[24] Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; Raza, N.; Park, C.; Ahmadian, A.; Salahshour, S., The generalized complex Ginzburg-Landau model and its dark and bright soliton solutions, Eur. Phys. J. Plus, 136, 7, 1-12 (2021)
[25] Yao, S. W.; Akinyemi, L.; Mirzazadeh, M.; Inc, M.; Hosseini, K.; Şenol, M., Dynamics of optical solitons in higher-order Sasa-Satsuma equation, Results Phys., 30, Article 104825 pp. (2021)
[26] Mirzazadeh, M.; Akbulut, A.; Taşcan, F.; Akinyemi, L., A novel integration approach to study the perturbed Biswas-Milovic equation with Kudryashov’s law of refractive index, Optik, 252, Article 168529 pp. (2022)
[27] Chen, Y. Q.; Tang, Y. H.; Manafian, J.; Rezazadeh, H.; Osman, M. S., Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model, Nonlinear Dyn., 105, 3, 2539-2548 (2021)
[28] Alquran, M.; Krishnan, E. V., Applications of sine-Gordon expansion method for a reliable treatment of some nonlinear wave equations, Nonlinear Stud., 23, 4, 639-649 (2016) · Zbl 1357.35082
[29] Akinyemi, L., Solutions of generalized fractional perturbed Zakharov-Kuznetsov equation arising in a magnetized dusty plasma, Rev. Mex. Fis., 67, 6, 1-14 (2021)
[30] Darvishi, M. T.; Najafi, M.; Wazwaz, A. M., Conformable space-time fractional nonlinear \((1 + 1)\)-dimensional Schrödinger-type models and their traveling wave solutions, Chaos Solitons Fractals, 150, Article 111187 pp. (2021) · Zbl 1498.35568
[31] Zhang, J.; Wei, X.; Lu, Y., A generalized \(( G^\prime / G)\)-expansion method and its applications, Phys. Lett. A, 372, 20, 3653-3658 (2008) · Zbl 1220.37070
[32] Ma, Y. L.; Wazwaz, A. M.; Li, B. Q., Novel bifurcation solitons for an extended Kadomtsev-Petviashvili equation in fluids, Phys. Lett. A, 413, Article 127585 pp. (2021) · Zbl 1528.35149
[33] Houwe, A.; Souleymanou, A.; Saliou, Y.; Inc, M.; Doka, S. Y.; Bouetou, T. B.; Bayram, M., Attitude of the modulation instability gain in oppositely directed coupler with the effects of the intrapulse Raman scattering and saturable function, Results Phys., 31, Article 104851 pp. (2021)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.