TY - JOUR A1 - Anco, Stephen A1 - Mohiuddin, Mohammad A1 - Wolf, Thomas T1 - Traveling waves and conservation laws for complex mKdV-type equations Y1 - 2012 U6 - https://doi.org/10.1016/j.amc.2012.06.061 VL - 219 IS - 2 SP - 679 EP - 698 ER - TY - JOUR A1 - Anco, Stephen A1 - Ali, Sajid A1 - Wolf, Thomas T1 - Exact Solutions of Nonlinear Partial Differential Equations by the Method of Group Foliation Reduction JF - SIGMA 7 N2 - A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. The method uses a separation ansatz to solve an equivalent first-order group foliation system whose independent and dependent variables respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries for the reaction-diffusion equation. With this group-foliation reduction method, solutions of the reaction-diffusion equation are obtained in an explicit form, including group-invariant similarity solutions and travelling-wave solutions, as well as dynamically interesting solutions that are not invariant under any of the point symmetries admitted by this equation. Y1 - 2011 U6 - https://doi.org/10.3842/SIGMA.2011.066 ER - TY - JOUR A1 - Wolf, Thomas A1 - Efimovskaya, Olga T1 - On Integrability of the Kontsevich Non-Abelian ODE System JF - Letters in Mathematical Physics Y1 - 2012 U6 - https://doi.org/10.1007/s11005-011-0527-4 VL - 100 IS - 2 SP - 161 EP - 170 ER - TY - JOUR A1 - Anco, Stephen A1 - Ali, Sajid A1 - Wolf, Thomas T1 - Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions JF - Journal of Mathematical Analysis and Applications Y1 - 2011 U6 - https://doi.org/10.1016/j.jmaa.2011.01.073 VL - 379 IS - 2 SP - 748 EP - 763 ER - TY - JOUR A1 - Wolf, Thomas T1 - A Dynamical Systems Approach for Static Evaluation in Go JF - Computational Intelligence and AI in Games, IEEE Transactions on N2 - In the paper, arguments are given as to why the concept of static evaluation has the potential to be a useful extension to Monte Carlo tree search. A new concept of modeling static evaluation through a dynamical system is introduced and strengths and weaknesses are discussed. The general suitability of this approach is demonstrated. Y1 - 2011 U6 - https://doi.org/10.1109/TCIAIG.2011.2141669 VL - 3 IS - 2 SP - 129 EP - 141 ER - TY - JOUR A1 - Hussin, V. A1 - Kiselev, A. V. A1 - Krutov, A.O. A1 - Wolf, Thomas T1 - N=2 Supersymmetric a=4 - Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Bousinesq equation JF - Journal of Mathematical Physics Y1 - 2010 U6 - https://doi.org/10.1063/1.3447731 VL - 51 ER - TY - JOUR A1 - Wolf, Thomas T1 - Positions in the Game of Go as Complex Systems JF - Proceedings of 2009 IEEE Toronto International Conference (TIC-STH 2009) - Science and Technology for Humanity Y1 - 2009 SN - 978-1-4244-3878-5 ER - TY - JOUR A1 - Tsarev, Sergey A1 - Wolf, Thomas T1 - Hyperdeterminants as integrable discrete systems JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2009 U6 - https://doi.org//10.1088/1751-8113/42/45/454023 VL - 42 ER - TY - JOUR A1 - Odesskii, Alexander A1 - Wolf, Thomas T1 - Compatible quadratic Poisson brackets related to a family of elliptic curves JF - Journal of Geometry and Physics Y1 - 2013 SN - 0393-0440 VL - 63 IS - 0 SP - 107 EP - 117 ER - TY - JOUR A1 - Anco, Stephen A1 - MacNaughton, Steven A. A1 - Wolf, Thomas T1 - Conservation laws and symmetries of quasilinear radial wave equations in multi-dimensions JF - Journal of Mathematical Physics Y1 - 2012 U6 - https://doi.org/10.1063/1.4711814 VL - 53 IS - 5 ER - TY - JOUR A1 - Wolf, Thomas A1 - Schrüfer, Eberhard A1 - Webster, Kenneth T1 - Solving large linear algebraic systems in the context of integrable non-abelian Laurent ODEs JF - Programming and Computer Software Y1 - 2012 U6 - https://doi.org/10.1134/S0361768812020065 SN - 0361-7688 VL - 38 IS - 2 SP - 73 EP - 83 ER - TY - JOUR A1 - Euler, Marianna A1 - Euler, Norbert A1 - Wolf, Thomas T1 - The Two-Component Camassa-Holm Equations CH(2,1) and CH(2,2): First-Order Integrating Factors and Conservation Laws JF - Journal of Nonlinear Mathematical Physics N2 - Recently, Holm and Ivanov, proposed and studied a class of multi-component generalizations of the Camassa–Holm equations [D. D. Holm and R. I. Ivanov, Multi-component generalizations of the CH equation: geometrical aspects, peakons and numerical examples, J. Phys A: Math. Theor. 43 (2010) 492001 (20pp)]. We consider two of those systems, denoted by Holm and Ivanov by CH(2,1) and CH(2,2), and report a class of integrating factors and its corresponding conservation laws for these two systems. In particular, we obtain the complete set of first-order integrating factors for the systems in Cauchy–Kovalevskaya form and evaluate the corresponding sets of conservation laws for CH(2,1) and CH(2,2). Y1 - 2013 U6 - https://doi.org/10.1142/S1402925112400025 VL - 19 IS - 1 SP - 13 EP - 22 ER -