Browsing by Author "Ullah, Malik Zaka"
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Item Lie symmetry analysis and exact solutions to N-coupled nonlinear Schrodinger’s equations with kerr and parabolic law nonlinearities(Editura Acad Romane, 2018) Triki, Houria; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Biswas, Anjan; Belic, Milivo; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4443-3337; 0000-0003-4732-5753; HTO-9875-2023; AAG-9947-2021; 56988856400; 23471031300This paper addresses N-coupled nonlinear Schrodinger's equation with spatio-temporal dispersion for Kerr and parabolic laws of nonlinearity by the aid of Lie symmetry analysis. We systematically construct similarity reductions to the derived ordinary differential equations by Lie group analysis. These equations lead to exact solutions.Item Optical soliton perturbation for complex Ginzburg–Landau equation with modified simple equation method(Elsevier, 2017-12-26) Biswas, Anjan; Triki, Houria; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 56988856400; 23471031300The modified simple equation method applied to perturbed complex Ginzburg-Landau equation gives dark and singular solutions to the model. The perturbation terms appear with full nonlinearity. There are eight nonlinear forms studied in this paper. These solitons appear with constraint conditions that gurantee its existence and these are also presented.Item Optical soliton perturbation with complex Ginzburg–Landau equation using trial solution approach(Elsevier, 2018-01-31) Biswas, Anjan; Triki, Houria; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 56988856400; 23471031300This paper retrieves optical soliton solution to the perturbed complex Ginzburg-Landau equation that is studied with nine different forms of nonlinearity. The trial solutions approach is the integration algorithm adopted in this paper. The perturbation terms appear with full nonlinearity to get a taste of generalized setting. Bright, dark and singular soliton solutions are obtained. The existence criteria of such solitons are also presented.Item Optical soliton perturbation with full nonlinearity by trial equation method(Elsevier, 2018) Biswas, Anjan; Triki, Houria; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4443-3337; HTO-9875-2023; AAG-9947-2021; 56988856400; 23471031300This paper studies optical soliton perturbation with spatio-temporal dispersion by trial equation method. There are five types of nonlinear fibers studied in this paper. They are quadratic-cubic law, anti-cubic law, cubic-quintic-septic law, triple-power law and log-law. Bright, dark and singular soliton solutions are recovered. In addition, singular periodic solutions naturally emerge as a byproduct of this integration mechanism.Item Optical soliton perturbation with full nonlinearity for Gerdjikov–Ivanov equation by trial equation method(Elsevier, 2017-12-20) Biswas, Anjan; Triki, Houria; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 56988856400; 23471031300This paper obtains optical soliton solution to perturbed Gerdjikov-Ivanov equation by trial equation approach. Bright, dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also emerge of this integration scheme.Item Optical soliton perturbation with full nonlinearity for Kundu–Eckhaus equation by modified simple equation method(Elsevier, 2018) Biswas, Anjan; Triki, Houria; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0003-4443-3337; 0000-0003-4732-5753; HTO-9875-2023; AAG-9947-2021; 56988856400; 23471031300This paper secures dark and singular optical soliton solution to the perturbed Kundu-Eckhaus equation where the perturbation terms appear with full nonlinearity. The integration algorithm adopted in this paper is the modified simple equation approach. The solitons appear with certain parameter restrictions that are listed as constraints.Item Optical soliton perturbation with full nonlinearity in polarization preserving fibers using trial equation method(National Institute for Optoelectronics, 2018) Biswas, Anjan; Triki, Houria; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.; 0000-0003-4732-5753; 0000-0003-4443-3337; HTO-9875-2023; AAG-9947-2021; 56988856400; 23471031300This paper obtains optical soliton solution to perturbed nonlinear SchrOdinger's equation by trial equation approach. There are nine types of nonlinear fibers studied in this paper. They are Kerr-law, power-law, quadratic-cubic law, parabolic-law, dual-power law, log-law, anti-cubic law, cubic-quintic-septic law and triple-power law. Bright, dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.Item Optical soliton perturbation with Gerdjikov–Ivanov equation by modified simple equation method(Elsevier, 2017-12-20) Biswas, Anjan; Triki, Houria; Alshomrani, Ali Saleh; Ullah, Malik Zaka; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 56988856400; 23471031300The modified simple equation scheme is employed to secure dark and singular optical soliton solution to the perturbed Gerdjikov-Ivanov equation that models pulse dynamics in optical fibers and PCF. The solvability conditions for this algorithm is also presented.Item Optical solitons and conservation law of Kundu-Eckhaus equation(Elsevier, 2017-10-18) Mirzazadeh, Mohammad; Triki, Houria; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Seadawy, Aly R.; Biswas, Anjan; Belic, Milivoj; Yıldırım, Yakup; Yaşar, Emrullah; Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Anabilim Dalı.; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 23471031300; 56988856400This paper obtains optical soliton solutions to the Kundu Eckhaus equation with general coefficients. The Riccati Bernoulli's sub-ODE method as well as Kudryashov's scheme are employed to obtain soliton solutions to the model. This generalized earlier reported result of the model with specific coefficients. Subsequently, the multiplier approach was utilized to secure a conserved quantity with the bright soliton solution that was reported earlier.Item Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method(Elsevier, 2017-11) Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj; Yaşar, Emrullah; Yıldırım, Yakup; Uludağ Üniversitesi/Fen-Edebiyet Fakültesi/Matematik Bölümü.; 0000-0003-4732-5753; AAG-9947-2021; 23471031300; 56988856400This paper obtains optical soliton solution to perturbed nonlinear Schrodinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.