# integrable integrable

# integrable Sentence Examples

• If we adopt this hypothesis, and substitute s= 2C T, where c is a constant, in the fundamental equation (9), we obtain at once d 2 E/d T 2 = - 2 (c' -c"), which is immediately integrable, and gives dE/dt=p = 2 (t ° -t) (c'-c") .1 (m) E1_,'=(t-t') (c'-c") 12to-(t-}-t')1 (11) where t o is the temperature of the neutral point at which dE/dt = o.

• If c is the velocity of radiation in free space and, u the refractive index of a transparent body, V= c/ï¿½; thus it is the expression c2 fï¿½ 2 (u'dx-}-v'dy+w'dz) that is to be integrable explicitly, where now (u',v',w') is what is added to V owing to the velocity (u,v,w) of the medium.

• Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (ï¿½2u',ï¿½2vi,ï¿½2w') is the gradient of a continuous function.

• If we eliminate P, Q, R from (22), the resulting equations are integrable with respect to t; thus Moa - M0a.

• Hamiltonian theory is an important element of integrable systems, whether discrete, ordinary differential or partial differential equations.

• integrable lattice equations, which are the difference analogs of the soliton equations.

• integrable systems to surface theory.

• integrable quantum field theory in the Hilary term of 2006.

• integrable maps.

• integrable functions over the space with respect to the prior measure.

• integrable QFT in presence of a boundary.

• They soon realized that the three body problem is not integrable, which means that no exact solution can ever be found.

• We study the homoclinic orbits of the completely integrable discrete sine-Gordon.

• singularity analysis The PainlevÃ© property has been used in many hundreds of papers to identify integrable cases of equations.

• torusroof that homoclinic trajectories in the form of pinched tori imply monodromy in two degree of freedom integrable systems has also been given.

• If c is the velocity of radiation in free space and, u the refractive index of a transparent body, V= c/Ã¯¿½; thus it is the expression c2 fÃ¯¿½ 2 (u'dx-}-v'dy+w'dz) that is to be integrable explicitly, where now (u',v',w') is what is added to V owing to the velocity (u,v,w) of the medium.

• Now the expression above given cannot be integrable exactly, under all circumstances and whatever be the axes of co-ordinates, unless (Ã¯¿½2u',Ã¯¿½2vi,Ã¯¿½2w') is the gradient of a continuous function.

• If we eliminate P, Q, R from (22), the resulting equations are integrable with respect to t; thus Moa - M0a.

• If we adopt this hypothesis, and substitute s= 2C T, where c is a constant, in the fundamental equation (9), we obtain at once d 2 E/d T 2 = - 2 (c' -c"), which is immediately integrable, and gives dE/dt=p = 2 (t Ã‚° -t) (c'-c") .1 (m) E1_,'=(t-t') (c'-c") 12to-(t-}-t')1 (11) where t o is the temperature of the neutral point at which dE/dt = o.

• Exact solutions and singularity analysis The PainlevÃ© property has been used in many hundreds of papers to identify integrable cases of equations.

• A proof that homoclinic trajectories in the form of pinched tori imply monodromy in two degree of freedom integrable systems has also been given.