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All Journal Journal of Tropical Life Science : International Journal of Theoretical, Experimental, and Applied Life Sciences The Journal of Experimental Life Sciences (JELS) Jurnal Mahasiswa Matematika Journal of Degraded and Mining Lands Management Journal of Natural A Jurnal Teknik Industri: Jurnal Keilmuan dan Aplikasi Teknik Industri Communication in Biomathematical Sciences
Suryanto, Agus
Biomathematics Research Group, Department Of Mathematics, University Of Brawijaya, Malang 65145
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Computer Science & IT Environmental Science Immunology & microbiology Industrial & Manufacturing Engineering Mathematics Medicine & Pharmacology Neuroscience Social Sciences

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Journal : Journal of Natural A

 1 
Effect of Energy Gain and Loss in Breathing Pattern of Solitary Wave for Nonlinear Equation Nur Shafika Abel Razali; Farah Aini Abdullah; Yahya Abu Hasan; Agus Suryanto
Journal of Natural A Vol 1, No 2 (2014)
Publisher : Fakultas MIPA Universitas Brawijaya

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Abstract

Nonlinear phenomena like soliton propagate over long distance in transmit information, without dispersion energy due to the properties of the solitons, which has balanced of the nonlinearity effect and dispersion effect resulted the signal undistorted and symmetric bell shape curve. We study about the properties and breathing pattern of solitary wave of pulses in absence and present of energy loss, by using one dimensional nonlinear equation; cubic-quintic complex Ginzburg-Landau equation (cqCGLE). Breathing pattern of soliton behaviour is constructed with hyperbolic sine and hyperbolic tangent as initial amplitude profile and observed by means of numerical simulation. Resulting in observation of breathing pattern of soliton in term of energy loss and gain while travelling, but it still maintains spatial localization of wave energy in the changing pulses shape through a unique dissipative soliton.Keywords— Soliton, nonlinearity, dispersion, breathing, energy.
A Variational Approach of Creeping Solitons with Hartman-Grobman Theorem in Complex Ginzburg-Landau Equation Nur Izzati Khairudin; Farah Aini Abdullah; Yahya Abu Hassan; Agus Suryanto
Journal of Natural A Vol 1, No 2 (2014)
Publisher : Fakultas MIPA Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (866.186 KB)

Abstract

The behavior of quintic nonlinear dispersion coefficient of creeping soliton in a spatial domain with hyperbolicity analysis of Hartman-Grobman Theorem by using variational approach is studied. Complex Ginzburg-Landau equation (CGLE) is used in the analysis as we relate the creeping soliton with Hartman- Grobman Theorem. We evaluated our work based on perturbed Jacobian matrix from system of three supercritical ordinary differential Euler-Lagrange equations, in which the eigenvalues of the stability matrix touch the imaginary axis. As a consequence in unfolding the bifurcation of creeping solitons, the equilibrium structure ultimately chaotic at the variation of the coefficient µ away from the critical value, µc . This leads to hyperbolicity loss of Hartman-Grobman Theorem in the dissipative system driven out the oscillatory instability of µ exceeded the criticality parameter corresponding to the Hopf bifurcations as the system is highly complex. This overall approach restrict to numerical investigation of the space time hyperbolic variation of CGLE.Keywords— Dissipative solitons, complex Ginzburg-Landau equation.
Co-Authors A.S. Adhiwibawa, Marcelinus Abdul Latif Al Fauzi Alghofari, Abdul Rouf Anam, Syaiful Brian Rahardi Darti, Isnani Farah Aini Abdullah Farah Aini Abdullah Hadi Susanto Hasan S. Panigoro Hidayat, Noor Hikmah, Maziyahtul Isnani Darti Isnani Darti Kartika Nugraheni Kestrilia Rega Prilianti Kusumahwinahyu, Wuryansari Muharini Luchman Hakim Musafir, Raqqasyi Rahmatullah Nur Izzati Khairudin Nur Shafika Abel Razali Onggara, Ivan C. Rima Anissa Pratiwi Rio Satriyantara Serafinah Indriyani Tatas H.P. Brotosudarmo Trisilowati, Trisilowati Wibowo, Ratno Bagus Edy Wuryansari Muharini Kusumahwinahyu Yahya Abu Hasan Yahya Abu Hassan