@article{MTMT:33310236,
	title = {New results of positive doubly periodic solutions to telegraph equations},
	url = {https://m2.mtmt.hu/api/publication/33310236},
	author = {Deng, Nan and Feng, Meiqiang},
	doi = {10.3934/era.2022059},
	journal-iso = {ELECTRON RES ARCH},
	journal = {ELECTRONIC RESEARCH ARCHIVE},
	volume = {30},
	unique-id = {33310236},
	abstract = {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.},
	keywords = {EXISTENCE; UNIQUENESS; Telegraph equation; Hilbert's metric; nontrivial doubly periodic solution; Eigenvalue theory; multiplicity and asymptotic behavior},
	year = {2022},
	eissn = {2688-1594},
	pages = {1104-1125}
}

@article{MTMT:33310235,
	title = {Multiple positive doubly periodic solutions to nonlinear telegraph systems},
	url = {https://m2.mtmt.hu/api/publication/33310235},
	author = {Feng, Meiqiang and Deng, Nan},
	doi = {10.1016/j.aml.2022.108233},
	journal-iso = {APPL MATH LETT},
	journal = {APPLIED MATHEMATICS LETTERS},
	volume = {133},
	unique-id = {33310235},
	issn = {0893-9659},
	abstract = {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.},
	keywords = {Multiplicity; Nonlinear telegraph systems; Doubly periodic solution},
	year = {2022},
	eissn = {1873-5452}
}

@article{MTMT:33310237,
	title = {Investigation on the Single and Multiple Dromions for Nonlinear Telegraph Equation in Electrical Transmission Line},
	url = {https://m2.mtmt.hu/api/publication/33310237},
	author = {Rizvi, Syed Tahir Raza and Ali, Kashif and Bekir, Ahmet and Nawaz, Badar and Younis, M.},
	doi = {10.1007/s12346-021-00547-w},
	journal-iso = {QUAL THEORY DYN SYST},
	journal = {QUALITATIVE THEORY OF DYNAMICAL SYSTEMS},
	volume = {21},
	unique-id = {33310237},
	issn = {1575-5460},
	abstract = {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).},
	keywords = {SOLITONS; INTEGRABILITY; Nonlinear Telegraph equation},
	year = {2022},
	eissn = {1662-3592},
	orcid-numbers = {Bekir, Ahmet/0000-0001-9394-4681}
}

@article{MTMT:31498534,
	title = {A novel analytic method for solving linear and non-linear telegraph equation},
	url = {https://m2.mtmt.hu/api/publication/31498534},
	author = {Al-Jaberi, Ahmed K. and Hameed, Ehsan M. and Abdul-Wahab, Mohammed S.},
	journal-iso = {PERIODICO TCHE QUIMICA},
	journal = {PERIODICO TCHE QUIMICA},
	volume = {17},
	unique-id = {31498534},
	issn = {1806-0374},
	abstract = {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.},
	keywords = {accuracy; Analytical solution; Hyperbolic Telegraph Equation; Taylors' Series; Non-Linear Operator},
	year = {2020},
	eissn = {2179-0302},
	pages = {536-548}
}

@article{MTMT:31586253,
	title = {The asymptotic speed of reaction fronts in active reaction-diffusion systems},
	url = {https://m2.mtmt.hu/api/publication/31586253},
	author = {Demaerel, Thibaut and Maes, Christian},
	doi = {10.1088/1751-8121/ab1d8d},
	journal-iso = {J PHYS A-MATH THEOR},
	journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
	volume = {52},
	unique-id = {31586253},
	issn = {1751-8113},
	abstract = {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.},
	keywords = {Reaction-diffusion; active matter; speed-selection},
	year = {2019},
	eissn = {1751-8121},
	orcid-numbers = {Maes, Christian/0000-0002-0188-697X}
}

@article{MTMT:31586252,
	title = {On the Consistency of the Reaction-Telegraph Process Within Finite Domains},
	url = {https://m2.mtmt.hu/api/publication/31586252},
	author = {Tilles, Paulo F. C. and Petrovskii, Sergei V.},
	doi = {10.1007/s10955-019-02379-0},
	journal-iso = {J STAT PHYS},
	journal = {JOURNAL OF STATISTICAL PHYSICS},
	volume = {177},
	unique-id = {31586252},
	issn = {0022-4715},
	abstract = {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.},
	keywords = {nonnegativity; Reaction-telegraph equation; Reaction-Cattaneo system; Robin boundary conditions},
	year = {2019},
	eissn = {1572-9613},
	pages = {569-587}
}

@article{MTMT:34714455,
	title = {Computation and stability of traveling waves in second order evolution equations},
	url = {https://m2.mtmt.hu/api/publication/34714455},
	author = {Beyn, W.-J. and Otten, D. and Rottmann-Matthes, J.},
	doi = {10.1137/16M108286X},
	journal-iso = {SIAM J NUMER ANAL},
	journal = {SIAM JOURNAL ON NUMERICAL ANALYSIS},
	volume = {56},
	unique-id = {34714455},
	issn = {0036-1429},
	year = {2018},
	eissn = {1095-7170},
	pages = {1786-1817}
}

@article{MTMT:25623240,
	title = {Analytical and numerical investigation of traveling waves for the Allen-Cahn model with relaxation},
	url = {https://m2.mtmt.hu/api/publication/25623240},
	author = {Lattanzio, Corrado and Mascia, Corrado and Plaza, Ramon G and Simeoni, Chiara},
	doi = {10.1142/S0218202516500226},
	journal-iso = {MATH MOD METH APPL S},
	journal = {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES},
	volume = {26},
	unique-id = {25623240},
	issn = {0218-2025},
	year = {2016},
	eissn = {1793-6314},
	pages = {x}
}

@article{MTMT:3033623,
	title = {On a nonlinear hyperbolic equation with a bistable reaction term},
	url = {https://m2.mtmt.hu/api/publication/3033623},
	author = {B H, Gilding and Kersner, Róbert},
	doi = {10.1016/j.na.2014.10.036},
	journal-iso = {NONLINEAR ANAL-THEOR},
	journal = {NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS},
	volume = {114},
	unique-id = {3033623},
	issn = {0362-546X},
	year = {2015},
	eissn = {1873-5215},
	pages = {169-185}
}

@article{MTMT:25496411,
	title = {Uniqueness and parameter dependence of positive doubly periodic solutions of nonlinear telegraph equations},
	url = {https://m2.mtmt.hu/api/publication/25496411},
	author = {Graef, JR and Kong, L and Wang, M},
	doi = {10.7494/OpMath.2014.34.2.363},
	journal-iso = {OPUSC MATHEMATICA},
	journal = {OPUSCULA MATHEMATICA},
	volume = {34},
	unique-id = {25496411},
	issn = {1232-9274},
	year = {2014},
	pages = {363-373}
}