By Jill McGivering BBC Asia analyst

Optimists hail it as the start of a new chapter. After months of careful diplomacy and groundwork, India's Prime Minister Atal Behari Vajpayee is heading to China.

Mr Vajpayee is still concerned about China's expansionism

He will be the first Indian prime minister on Chinese soil for 10 years.

India's Defence Minister George Fernandes has reportedly called it the "Let's be friends" trip.

But even while Mr Vajpayee was packing, doubts were being raised about whether he will return with a breakthrough in the long and usually troubled relationship between the two most populous countries in the world.

Mutual claims

It is more than 40 years since India and China last went to war but the wounds have never healed.

The long territorial disputes which have soured relations for decades have not been resolved.

Each country still claims territory held by the other.

China talks about a multipolar world but wants a unipolar Asia, with itself in prime position Political analyst

Joint working groups travel back and forth clutching maps but the shared border of more than 4,000 kilometres (2,500 miles) will take years to agree.

China stays angry about India's harbouring of the Dalai Lama and his Tibetan government-in-exile.

India stays angry about China's close relationship with Pakistan and, in particular, their military co-operation.

It is suggested that none of these core and deeply divisive issues will even be addressed during Mr Vajpayee's visit.

And without substantial progress, it is hard to imagine an end to the mutual suspicion which characterises Sino-Indian relations.

Political shifts

So why the sudden flurry of positive rhetoric from both sides?

It is due partly to the seismic shift in geopolitics.

China and India both watched the launch of the US war on terrorism with unease.

Admittedly, each has found a way of benefiting from it. China made the US include Uighur militants in Xinjiang in the general condemnation; India made sure Kashmiri militants were generally condemned too.

But the US military action, first in Afghanistan and then in Iraq, alarmed both governments.

Helping each other

They were cautious in expressing opposition - but opposed action nonetheless.

One protection against this newly dominant US could be for India and China to look to each other.

Mr Vajpayee's host Wen Jiabao may find it hard to win his guest round

Much of China's recent rhetoric seems to suggest just such a new strategic alliance with India.

Beijing has a particular interest at heart. It is concerned by the growing military co-operation between Delhi and Washington.

The suggestion that India could act as a friendly host for the US in a future Asian crisis seems less absurd - a crisis which could well involve China on the "other" side in conflict with, for example, Taiwan or Japan.

China is eager to prove a counterweight to any such plan.

But Beijing will find it hard to win India round.

The mistrust is deeply engrained. India developed its nuclear programmes largely with China in mind.

When Defence Minister George Fernandes referred to China some years ago as India's "enemy number one", he voiced a view common in Delhi.

Many are still cynical about China's expansionist agenda.

As one analyst put it: "China talks about a multipolar world but wants a unipolar Asia, with itself in prime position."

Joint ventures

Even if there is little political progress, both countries can agree on trade.

Mr Vajpayee is taking a substantial business delegation.

There is talk about new joint ventures and an easing of restrictions.

India is increasingly feeling pressure from China's manufacturing sector.

Cut-price mass-produced Chinese goods flooding into India are showing India's inability to compete.

India wants to learn more. China, for its part, has watched India's phenomenal international success in IT and the call centre and service centre sectors. It is eager for joint ventures so it can learn and follow suit.

The total volume of formal trade is modest, just $5bn a year, although black market trade across the porous border adds an invisible extra.

Officials are talking about tripling formal trade by 2010.