TY - JOUR AU - Deng, Nan AU - Feng, Meiqiang TI - New results of positive doubly periodic solutions to telegraph equations JF - ELECTRONIC RESEARCH ARCHIVE J2 - ELECTRON RES ARCH VL - 30 PY - 2022 IS - 3 SP - 1104 EP - 1125 PG - 22 SN - 2688-1594 DO - 10.3934/era.2022059 UR - https://m2.mtmt.hu/api/publication/33310236 ID - 33310236 N1 - Funding Agency and Grant Number: Beijing Natural Science Foundation of China [1212003]; promoting the classified development of colleges and universities-application and cultivation of scientific research awards of BISTU [2021JLPY408] Funding text: This work is sponsored by the Beijing Natural Science Foundation of China (1212003) and the promoting the classified development of colleges and universities-application and cultivation of scientific research awards of BISTU (2021JLPY408) . AB - The paper is devoted to obtain new results of positive doubly periodic solutions to telegraph equations. One of the interesting features in our proof is that we give a new attempt to solve telegraph equation by using the theory of Hilbert's metric. Then we apply the eigenvalue theory to analyze the existence, multiplicity, nonexistence and asymptotic behavior of positive doubly periodic solutions. We also study a corresponding eigenvalue problem in a more general case. LA - English DB - MTMT ER - TY - JOUR AU - Feng, Meiqiang AU - Deng, Nan TI - Multiple positive doubly periodic solutions to nonlinear telegraph systems JF - APPLIED MATHEMATICS LETTERS J2 - APPL MATH LETT VL - 133 PY - 2022 PG - 6 SN - 0893-9659 DO - 10.1016/j.aml.2022.108233 UR - https://m2.mtmt.hu/api/publication/33310235 ID - 33310235 N1 - Funding Agency and Grant Number: Beijing Natural Science Foundation [1212003] Funding text: This work is sponsored by Beijing Natural Science Foundation under Grant No. 1212003. Both the authors would like to express their gratitude to the referee for valuable comments and suggestions. AB - Our primary objective of this article is to study a class of nonlinear telegraph systems. Some new criteria for the existence and multiplicity of positive doubly periodic solutions are established. Many positive doubly periodic solutions are also considered. (C) 2022 Elsevier Ltd. All rights reserved. LA - English DB - MTMT ER - TY - JOUR AU - Rizvi, Syed Tahir Raza AU - Ali, Kashif AU - Bekir, Ahmet AU - Nawaz, Badar AU - Younis, M. TI - Investigation on the Single and Multiple Dromions for Nonlinear Telegraph Equation in Electrical Transmission Line JF - QUALITATIVE THEORY OF DYNAMICAL SYSTEMS J2 - QUAL THEORY DYN SYST VL - 21 PY - 2022 IS - 1 PG - 14 SN - 1575-5460 DO - 10.1007/s12346-021-00547-w UR - https://m2.mtmt.hu/api/publication/33310237 ID - 33310237 N1 - Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Islamabad, Pakistan Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, Eskisehir, 26030, Turkey Department of Computer Science, University of the Punjab, Lahore, Pakistan Cited By :11 Export Date: 1 March 2024 Correspondence Address: Bekir, A.; Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, Turkey AB - In this paper, we study some soliton solutions for a nonlinear Telegraph equation (NLTE), also known as the damped wave equation studied in electrical transmission line. We analyze one soliton transformation, two soliton interaction, three soliton interaction and N-soliton interactions for NLTE with the help of Hirota bilinear method (HBM). To enhance the quality of information carriers in fibers, we can place two solitons close to one another in a single channel of an optical fiber and also suppress their mutual interaction. We also obtain Jacobi elliptic solutions (JES) and other solitary wave solutions which degenerate to kink, bell type, rational and dark solitons for NLTE with the aid of extended trial function scheme (ETFS). LA - English DB - MTMT ER - TY - JOUR AU - Al-Jaberi, Ahmed K. AU - Hameed, Ehsan M. AU - Abdul-Wahab, Mohammed S. TI - A novel analytic method for solving linear and non-linear telegraph equation JF - PERIODICO TCHE QUIMICA J2 - PERIODICO TCHE QUIMICA VL - 17 PY - 2020 IS - 35 SP - 536 EP - 548 PG - 13 SN - 1806-0374 UR - https://m2.mtmt.hu/api/publication/31498534 ID - 31498534 AB - The modeling of many phenomena in various fields such as mathematics, physics, chemistry, engineering, biology, and astronomy is done by the nonlinear partial differential equations (PDE). The hyperbolic telegraph equation is one of them, where it describes the vibrations of structures (e.g., buildings, beams, and machines) and are the basis for fundamental equations of atomic physics. There are several analytical and numerical methods are used to solve the telegraph equation. An analytical solution considers framing the problem in a well-understood form and calculating the exact resolution. It also helps to understand the answers to the problem in terms of accuracy and convergence. These analytic methods have limitations with accuracy and convergence. Therefore, a novel analytic approximate method is proposed to deal with constraints in this paper. This method uses the Taylors' series in its derivation. The proposed method has used for solving the second-order, hyperbolic equation (Telegraph equation) with the initial condition. Three examples have presented to check the effectiveness, accuracy, and convergence of the method. The solutions of the proposed method also compared with those obtained by the Adomian decomposition method (ADM), and the Homotopy analysis method (HAM). The technique is easy to implement and produces accurate results. In particular, these results display that the proposed method is efficient and better than the other methods in terms of accuracy and convergence. LA - English DB - MTMT ER - TY - JOUR AU - Demaerel, Thibaut AU - Maes, Christian TI - The asymptotic speed of reaction fronts in active reaction-diffusion systems JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 52 PY - 2019 IS - 24 PG - 13 SN - 1751-8113 DO - 10.1088/1751-8121/ab1d8d UR - https://m2.mtmt.hu/api/publication/31586253 ID - 31586253 N1 - Cited By :4 Export Date: 1 March 2024 AB - We study various combinations of active diffusion with branching, as an extension of standard reaction-diffusion processes. We concentrate on the selection of the asymptotic wavefront speed for thermal run-and-tumble and for thermal active Brownian processes in general spatial dimensions. Comparing 1D active branching processes with a passive counterpart (which has the same effective diffusion constant and reproduction rate), we find that the active process has a smaller propagation speed. In higher dimensions, a similar comparison yields the opposite conclusion. LA - English DB - MTMT ER - TY - JOUR AU - Tilles, Paulo F. C. AU - Petrovskii, Sergei V. TI - On the Consistency of the Reaction-Telegraph Process Within Finite Domains JF - JOURNAL OF STATISTICAL PHYSICS J2 - J STAT PHYS VL - 177 PY - 2019 IS - 4 SP - 569 EP - 587 PG - 19 SN - 0022-4715 DO - 10.1007/s10955-019-02379-0 UR - https://m2.mtmt.hu/api/publication/31586252 ID - 31586252 N1 - Funding Agency and Grant Number: Royal Society (UK) [NF161377]; RUDN University Program 5-100 Funding text: This work was supported by The Royal Society (UK) through the Grant No. NF161377 (to P.F.C.T and S.V.P.). The publication has been prepared with the support of the "RUDN University Program 5-100" (to S.V.P.). AB - Reaction-telegraph equation (RTE) is a mathematical model that has often been used to describe natural phenomena, with specific applications ranging from physics to social sciences. In particular, in the context of ecology, it is believed to be a more realistic model to describe animal movement than the more traditional approach based on the reaction-diffusion equations. Indeed, the reaction-telegraph equation arises from more realistic microscopic assumptions about individual animal movement (the correlated random walk) and hence could be expected to be more relevant than the diffusion-type models that assume the simple, unbiased Brownian motion. However, the RTE has one significant drawback as its solutions are not positively defined. It is not clear at which stage of the RTE derivation the realism of the microscopic description is lost and/or whether the RTE can somehow be 'improved' to guarantee the solutions positivity. Here we show that the origin of the problem is twofold. Firstly, the RTE is not fully equivalent to the Cattaneo system from which it is obtained; the equivalence can only be achieved in a certain parameter range and only for the initial conditions containing a finite number of Fourier modes. Secondly, the Dirichlet type boundary conditions routinely used for reaction-diffusion equations appear to be meaningless if used for the RTE resulting in solutions with unrealistic properties. We conclude that, for the positivity to be regained, one has to use the Cattaneo system with boundary conditions of Robin type or Neumann type, and we show how relevant classes of solutions can be obtained. LA - English DB - MTMT ER - TY - JOUR AU - Beyn, W.-J. AU - Otten, D. AU - Rottmann-Matthes, J. TI - Computation and stability of traveling waves in second order evolution equations JF - SIAM JOURNAL ON NUMERICAL ANALYSIS J2 - SIAM J NUMER ANAL VL - 56 PY - 2018 IS - 3 SP - 1786 EP - 1817 PG - 32 SN - 0036-1429 DO - 10.1137/16M108286X UR - https://m2.mtmt.hu/api/publication/34714455 ID - 34714455 N1 - Department of Mathematics, Bielefeld University, Bielefeld, Germany Institute for Analysis, Karlsruhe Institute of Technology, Karlsruhe, Germany Cited By :4 Export Date: 1 March 2024 CODEN: SJNAA LA - English DB - MTMT ER - TY - JOUR AU - Lattanzio, Corrado AU - Mascia, Corrado AU - Plaza, Ramon G AU - Simeoni, Chiara TI - Analytical and numerical investigation of traveling waves for the Allen-Cahn model with relaxation JF - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES J2 - MATH MOD METH APPL S VL - 26 PY - 2016 IS - 5 SP - x PG - 55 SN - 0218-2025 DO - 10.1142/S0218202516500226 UR - https://m2.mtmt.hu/api/publication/25623240 ID - 25623240 N1 - Funding Agency and Grant Number: Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila; MathMods Program (Erasmus Mundus); CONACyT (Mexico); MIUR (Italy), through the MAE Program for Bilateral Research [146529]; Italian Project FIRB "Dispersive Dynamics: Fourier Analysis and Variational Methods" Funding text: R.G.P. is grateful to the Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, and to the MathMods Program (Erasmus Mundus) for their hospitality and financial support in academic visits during the Falls of 2012 and 2013, when this research was carried out. This work was partially supported by CONACyT (Mexico) and MIUR (Italy), through the MAE Program for Bilateral Research, Grant No. 146529 and by the Italian Project FIRB 2012 "Dispersive Dynamics: Fourier Analysis and Variational Methods". LA - English DB - MTMT ER - TY - JOUR AU - B H, Gilding AU - Kersner, Róbert TI - On a nonlinear hyperbolic equation with a bistable reaction term JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 114 PY - 2015 SP - 169 EP - 185 PG - 17 SN - 0362-546X DO - 10.1016/j.na.2014.10.036 UR - https://m2.mtmt.hu/api/publication/3033623 ID - 3033623 N1 - Export Date: 1 March 2024 CODEN: NOAND Correspondence Address: Gilding, B.H.; Department of Mathematics, College of Science, Kuwait University, P.O. Box 5969, Kuwait LA - English DB - MTMT ER - TY - JOUR AU - Graef, JR AU - Kong, L AU - Wang, M TI - Uniqueness and parameter dependence of positive doubly periodic solutions of nonlinear telegraph equations JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 34 PY - 2014 IS - 2 SP - 363 EP - 373 PG - 11 SN - 1232-9274 DO - 10.7494/OpMath.2014.34.2.363 UR - https://m2.mtmt.hu/api/publication/25496411 ID - 25496411 N1 - Cited By :1 Export Date: 1 March 2024 LA - English DB - MTMT ER -