Access the full text.
Sign up today, get unlimited access with DeepDyve Pro!
strategies [24–32]. Players with memory- one strategies respond to the outcome of the previous round only. Such strategies can be written as a vector p = (pCC, pCD, pDC, pDD) in the 4- dimensional cube [0, 1]4 ...
the statement of scale symmetry (11), we set λ = 1+ϵ, where ϵ is an arbitrarily small constant. This allows for any scale transformation to be constructed by sequentially applying such infinitesimal ...
caused by the cubic terms, unless the integration region is altered to some non-trivial complex one . Another important reason is that the highlighting mechanism of symmetries explained in Sect. 3 requires ...
is defined by some solution to (2). One easily checks that the following four vector fields are infinitesimal symmetries of (2): \begin{equation} \{T_1=\partial_u,\ T_2=\partial_v,\ D_1=u\partial_u+v\partial_v ...
. In 3D, for constraints of type ( ii ) we distinguish two cases. If the point P is not on the line L, the constraint removes one freedom and transforms as a vector along the perpendicular from L to P, which ...
some obstructions to such existence in terms of the local invariants of the Euler–Lagrange systems. In addition, we discover a class of Bäcklund transformations relating two hyperbolic Euler–Lagrange ...
of the Gross–Pitaevskii equation, as we discuss in Appendix. One symmetry is particularly interesting—a breather boost, which we found first described in [61]. This is self- transformation of the Gross–Pitaevskii ...
such transformations is finite- dimensional . Finally, in Section 5 we discuss some of the limitations of our approach. Although the classical literature on Bäcklund transformations —e.g. Goursat’s memoir [3]—was focused ...
. The procedure to find a local one -parameter group of transformation is available in literature (see details in [64–67]). In case of PDEs, the symmetries reduces the number of independent variables and transform ...
small because, in the discretized space, τ is so small that no point can switch from one bubble to another (i.e., ui changes from 0 to 1 or 1 to 0 for some i). On the other hand, for large τ ...
Access the full text.
Sign up today, get unlimited access with DeepDyve Pro!